Making A Math Murderer

Just think of all the questions that arise when a seemingly-healthy baby dies. Was there an illness that went undetected? Was there a rare genetic defect that couldn’t possibly have been known? Are any signs of physical trauma related to the resuscitation efforts of a fragile infant, or something more sinister? Every time a baby dies, police investigate with a host of complex questions to determine whether the death is natural and accidental, or… not. And the odds are anything but clear.
So what do we do when it happens twice to the same person? What are the odds of THAT?
A British mother named Sally Clark suffered two separate tragedies with the deaths of her infant sons. Her resulting trial for murder included expert testimony from Sir Roy Meadow, a noted expert on child abuse cases. And Meadow’s misuse of conditional probability painted Sally Clark as perpetrator rather than a victim.
Math is often theoretical, but sometimes doing it right is the difference between life and death.
** PARTIAL LIST OF SOURCES **
Ben-Israel, Adi. “Using Statistical Evidence in Courts: What Went Wrong in the Case of Sally Clark?” ben-israel.rutgers.edu/711/Sal...
Dyer, Clare. “Falsely Convicted Sally Clarke Dies Suddenly.” BMJ: British Medical Journal, vol. 334, no. 7594, BMJ, 2007, pp. 602-03, www.jstor.org/stable/20506708.
General Medical Council v. Meadow, England and Wales Court of Appeals (Civil Division), www.bailii.org/ew/cases/EWCA/C...
Nobles, Richard, and David Schiff. “A Story of Miscarriage: Law in the Media.” Journal of Law and Society, vol. 31, no. 2, [Cardiff University, Wiley], 2004, pp. 221-44, www.jstor.org/stable/1410525.
Scheurer, Vincent. “Convicted on Statistics?” understandinguncertainty.org/n...
Schneps, L., & Colmez, C. (2013). Math on trial: How numbers get used and abused in the courtroom. www.amazon.com/Math-Trial-Num...
Watkins SJ. Conviction by mathematical error? Doctors and lawyers should get probability theory right. BMJ. 2000;320(7226):2-3. www.ncbi.nlm.nih.gov/pmc/arti...
Webster, Richard. “Roy Meadow and the Statistics of Cot Deaths.” www.richardwebster.net/cotdeat...
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#education #vsauce #crime

[@blizzardaddict1383]

I know another joke: An engineer, a physicist and a statiscian go hunting in the woods. They spot a deer and take turns shooting at it, first goes the physicist, he look at the angle, calculates the speed of the bullet and shoots but his shot goes 50 meters to the right. The engineer says he didnt count for the wind and he also makes his measurement and shots but his shot goes 50 meters to the left. Then the statiscian yells hapilly : We did it !

[@Vsauce2]

Ok, that's a good one.

[@nxt6341]

in life, all boils down to a 50/50 chance

[@Phoboz]

@@nxt6341 I always but the lottery when I walk in front of someone selling, cus either I win or I lose. 50/50 chance of being rich yo.

[@nxt6341]

@@Phoboz exactly man, you either win or lose

[@magno415]

@@nxt6341 you dont have a brain or you have two i cant understand

[@counterfeit1148]

The "Two bombs on a plane is unlikely" thing at the end reminds me of the Blackadder episode where Baldrick says "You know how they say someone somewhere has a bullet with your name on it? Well if I own the bullet with my name on it, I'll never get hit by it because I won't shoot myself".

[@Vsauce2]

Blackadder is great. My favorite one is the dictionary episode.

[@thinboxdictator6720]

@@Vsauce2 please accept my most enthusiastic contrafibularities.

[@mulgerbill]

​@@Vsauce2 My most sincere contrafibularities to you good sir! But prithee, do not mention the Scottish Play!

[@adityasuhane8930]

I didn't got the joke? I mean why to keep a bomb in first place?

[@souravkb]

@@adityasuhane8930 since 'the odds two people having bomb is astronomical', if he has a bomb, then there is no chance of others around him having a bomb... So he is safe from bombs (unless his one explodes)

[@KarisMajik]

There's one woman who was arrested for poisoning her baby with antifreeze. She gave birth while incarcerated, the baby went into foster care, and also died with symptoms mimicking antifreeze poisoning. The cause turned out to be genetic

[@Inkbkank.2029]

Something is wrong with out system to charge her agin if it was genetic so why isn’t she servin* her other time ? …

[@Transformers2Fan1]

​​@@Inkbkank.2029your comment makes no sense If she's innocent, you think she SHOULD serve another sentence? And it said nothing about her being charged twice, just the first time.

[@daryncollins7640]

thats actually a mix of lucky and unlucky because if she didnt happen to be pregnant with another baby who had the same condition it probably would have never been discovered it was anything but murder

[@alexs6746]

Hitchhiker: how did you know I wasn’t a serial killer Driver: because the odds of two serial killers being in the same car are astronomical

[@neandrewthal]

The fact alone that they make the next child wear an apnea monitor obliterates the idea that the next instant death is just as improbable as the first.

[@Vsauce2]

Good point. The argument is built right into that.

[@TheNess667]

Yes i was just thinking about how researchers are now understanding more about SIDS and how sleep apnea and structural deformities of the eosophagus have a genetic component to them. Sadly some families may just be more prone to these tragedies than others without knowing why.

[@vibaj16]

I was thinking that it could be genetic, so there would be a higher chance that the 2nd also would have it

[@ezraho8449]

Yeah I was thinking this while watching the video. She must have the worst defense attorneys of all time for them not to catch any of this.

[@alaididnalid7660]

Well... technically it's not the wearing of the monitor, it's the fact that the monitor gave warnings.

[@D30TBrendon]

This is an incredible concept for a video series. Would love to see more real life math failures.

[@tiku80]

''Would love to see more real life math failures'' Are you sure?

[@HeadShotPR]

There's way too many real life math failures

[@AxxLAfriku]

Let me get this straight: You comment something that is unrelated to the fact that I have two HEAVENLY HANDSOME girlfriends? Considering that I am the unprettiest KZbinr ever, having two handsome girlfriends is really incredible. Yet you did not mention that at all. I am quite disappointed, dear bren

[@thenateman27]

Check out Matt Parkers new book. It's about math failures ranging from a small Oops, to mass death

[@thenateman27]

OH, and he mentions this exact case

[@Jabranalibabry]

Man, this breaks my heart. Imagine losing two children and then going through such hell. I hope her surviving son and husband are happy, she was a strong person to endure it all

[@biazacha]

I would have zero trust in the authorities if I was her son, they literally took his mom from him after the family already suffered so much.

[@Jabranalibabry]

@@biazacha Absolutely, brother, I think that's why it's very important for people in positions of power esp bureaucracies to know that there's a person behind every file and not make it 'routine'.

[@smartereveryday]

Closing with her words was powerful.

[@LudusArtifex]

Yes, you’re right.

[@gingerbread6356]

Smarter every day gets one reply?

[@RoseOnFire]

@@gingerbread6356 3*

[@ashleyjaytanna1953]

4+

[@missseaweed2462]

It was.

[@ChaosRaych]

This terribly tragic situation could be the best answer to anyone who asked, "When am I ever going to use this in real life?" during math class.

[@wolfgangoppenheimer2905]

Yes, it really annoys me to no end that people just ignore maths as " WhEn wILl i evER usE iT ".

[@jieyeongtan1351]

@@wolfgangoppenheimer2905 Well to be fair if they're asking that question they probably never will coz they won't know how to

[@MementoMoriGrizzly]

The people who say that, are too dumb to solve a school exercise, let alone use it in real life. It's a waste of time teaching them in the first place.

[@Vsauce2]

Unfortunately... yes.

[@Aki.0049]

@@jieyeongtan1351 won't stop them from pretending to, unfortunately

[@corrinking96]

This is a really sad video, this woman lost more than most of us could possibly imagine and then rather than anyone having sympathy for her she was convicted by a jury for a horrendous crime that she never committed, and its so much more unfortunate that she basically numbed herself to death from all the pain inflicted upon her. This world is cruel, and ive never hoped someone rested in more peace than i do for this woman.

[@zombies4u29]

Can't agree more. I hope her remaining family is over compensated for all they've lost

[@acediadekay3793]

I shed a tear reading your comment, can't even imagine the demons she have had after an experience so horrendous

[@user-vn7ce5ig1z]

Unfortunately, this wasn't the only time this sort of thing has happened, there have been numerous cases of people not only losing a loved one, but being accused of doing it and going to jail for it. 😒

[@ZentaBon]

I would've killed myself if convicted in a case like this.

[@JamecBond]

Cases like this, of backwards justice, are more common than most realize

[@livinginputnam8820]

From someone who's worked in the Child Protective Services field for over 20 years, I believe this is a must-see video for all CPS investigators. Thank you Kevin.

[@Indrid-Cold]

THE ONLY TRULY IMPORTANT QUESTION HERE, IS: What the FVCK was a statistician doing on the stand three years prior to THE CORONER with the results of the goddamned autopsy?!? Anyone have an answer for this? How and why did it take three years to find out that the child died of a bacterial infection????

[@orppranator5230]

@@Indrid-Cold Someone at CPS was trying to get promoted for taking down a supposed murderer, and was suppressing that evidence/testimony somehow?

[@KawaiiCat2]

Also for someone who works in early childhood education.

[@FREEDOMFORUKRAINE2024]

When he said "double infanticide is actually more rare than double COT" - Major BRUH moment.

[@travcollier]

Frequentist vs Bayesian... The latter approach is far more appropriate to this (and most real world) applications.

[@hsterts]

Im no statistician, but if someone had the history and previously had a reason to commit infanticide once, wouldnt the second occurrence be at least more probable?

[@travcollier]

@@hsterts I'm not certain, but I would presume so. The statisical term for it is "the events are not independent". If you roll 2 normal dice, the chance of getting 1,1 is just 1/6 × 1/6. But lots of things in life aren't like that. Committing infanticide twice is still a lot less common than having two babies dying of SIDS/COT.

[@jigan2971]

@@hsterts you're not accounting in for the probability of having a child after committing infanticide, would you expect someone to have a child after the first one?, and then there's the fact that, there can be genetic defects, where it would likely be probable for it to be reoccurring, it's like a mom has an albino child , and probability of one of the next few children being albino, in which, you'd expect more of a 1 in 4 chance, cause the parents carry a gene for albinism, compared to the 1 in 18,000 - 20,000 , the circumstances change the probability, so, you'd expect double COT to be more like, 1 in 34,172, assuming that the parents only carry one gene associated with COT, it can also be a case where they have multiple genes associated, which can ramp up chances of COT

[@taylor92493]

@jigan Just on the note of “not accounting for” everyone’s model might be slightly different and account for something they deem important. Might be hard to explain that model on KZbin.

[@TheFinalChapters]

The thing that sticks out the most to me as an American is the fact that you could have two jurors vote "not guilty" on murder charges and still have the verdict be "guilty".

[@Vsauce2]

Good point -- anywhere in the US she wouldn't have been convicted. Given what the UK press published about her, her life still probably would've been terrible, but at least she wouldn't have spent years in prison.

[@LilyoftheLake14]

Right!? I was wondering this too! Wouldn't a 10 to 2 vote be a "hung jury" in the US? Idk if they get the case dismissed as not guilty or if they just have a 2nd trial with a new jury at that point though. She definitely wouldn't have been convicted though. Even an 11 to 1 wouldn't have equaled to a conviction. 😔

[@Mythraen]

@@Vsauce2 I mean, I don't know how British courts work. If we just go off the jury of 12 and how they voted, you're right, but I'd want to know a lot more about their court system, and especially their jury system, before I declared, "she wouldn't have been convicted" in ours.

[@Vsauce3]

KEVIN! Love this video! It is such a unique way to express information while also telling a story. Great job!

[@almightyentertainment7333]

Can’t wait for season 3 of CYSTM

[@imabookworm]

Yay

[@Bibibosh]

Why does KZbin try to ruin everything good on this website.

[@NearlyBatman]

Sorry it got demonetized. And yes, it was definitely very interesting. What is also interesting is why there are only 4 comments here.

[@gunjanshah4844]

@@NearlyBatman 5* 😂

[@AdamOfIngolstadt]

"one is a tragedy, two is suspicious, three is murder" -man who accused woman of murder after 2 deaths

[@5GTower1000Percent]

Imagine losing 2 children and then being called a monster by people who only repeat flawed statistics they themself don't understand. On the other hand it is absolutely disgusting to see how an expert we are supposed to trust abuses his position of power and doesn't admit that he may actually be wrong when other experts question his calculations. My guess is, to solve this issue, that in medical cases the whole case should be checked by several independent groups of experts. These take months anyway, so having several independent groups of expert's check them would make it more clear if it is crystal clear or if critical information is needed.

[@tastes-like-straberries]

Agreed

[@Indrid-Cold]

THE ONLY TRULY IMPORTANT QUESTION HERE, IS: What the FVCK was a statistician doing on the stand three years prior to THE CORONER with the results of the goddamned autopsy?!? Anyone have an answer for this? How and why did it take three years to find out that the child died of a bacterial infection????

[@Soneoak]

The calculations are correct, the judge and jury have no idea what was happening and just passed judgement after being told of the likelihood equivalence and had no idea what they were doing. The expert isn't wrong, his data was wrongly applied.

[@nomekop777]

That 2nd paragraph hits hard. Also who's fauchi?

[@AnnekeOosterink]

The problem here is also, a pediatrician is not a statistician, so he was not an expert on those statistics, yet he was trusted to interpret them. Being skilled in one area does not make him skilled in another.

[@ryanhaart]

I live in the UK and remember this case very well, as it garnered a lot of publicity. At the time, when they talked about how unlikely two cot deaths were, I immediately thought "what about correlation"? Maybe cot death has some genetic causes or other correlations, or maybe there were some unknown toxins in the paint or furniture of the room where the babies slept.

[@adamrak7560]

Or mold spores from previous water damage. There are many bacteria and mold species which are perfectly harmless for a healthy adult, but quite deadly for a baby.

[@Treblaine]

It's the equivalent of accusing each and every lottery winner of cheating because "the chance of you winning is one in tens of millions" but tens of millions of people play the game!

[@jamesmccomb9525]

Nothing's changed since then and it never will in British society. People are all too eager to make the same mistakes.

[@Indrid-Cold]

THE ONLY TRULY IMPORTANT QUESTION HERE, IS: What the FVCK was a statistician doing on the stand three years prior to THE CORONER with the results of the goddamned autopsy?!? Anyone have an answer for this? How and why did it take three years to find out that the child died of a bacterial infection???? I suppose that’s too much to ask from a country where attorneys dress like penguins, and the judges still wear powdered wigs 🙄

[@feuby8480]

Yeah I though it too. I didn't already see the logic flaw of the calculus, but I knew something was wrong. Just because it's rare does not mean it never happens. And as you stated it, there are MANY, MANY reasons that could lead to two death. I first though the explanation was something like "the baby bed was inadequate", or they put a pillow that blocked baby's breathing. But seing that's because of infection make this way lot horrible.

[@Stars-Mine]

What baffles me so hard is why Meadows assumed the odds of a second instance was the same as a first instance. We still dont know the causes for SIDS and how exactly it functions, but we KNOW the conditions were met the first time meaning we know its possible it can happen again. LIke lets take a simpler example with better understood odds.. the odds of having a kid that is Schizophrenic is 1 in 100. but when you do hit that 1/100 roll, you know something in either the nature or nurture of the home environment raises the odds of a second kid to 1 in 10. So the odds of having two kids that are Schizophrenic is not 1/10k, its 1/1k. Every time new information is added to a statistical model, the model changes. because the odds were obfuscating unknown variables before.

[@SiMeGamer]

That's exactly the point of the video. It used the simplest form of consecutive odds multiplication and not the conditional form.

[@karlboud88]

wait, 2 of my 4 siblings are schizophrenic...

[@helderboymh]

@@karlboud88 are you sure you are not an only child ?

[@Dialethian]

@@helderboymh ???

[@helderboymh]

@@Dialethian it's a joke ;)

[@zantas-handle]

According to my local Crime Investigation Officer, the odds of your car being vandalised are only 1/220 in my city. But the odds of TWO cars in the same car park being vandalised are much higher, closer to 1/1500. So, whenever I park in the city, I always vandalise somebody's car in the same car park - y'know, just to be on the safe side.

[@noidea2568]

In my opinion, this is one of your best videos you've made to date. You explain everything very clearly, while telling a great but tragic story, showing how important maths can really be, and why it's important to understand certain concepts, because if we don't, then horrible thing can happen, and real people can be hurt by a simple mistake. Great work, I really appreciate it!

[@TheFaxMachine69]

Hearing that she got released made me so happy, then hearing she died honestly crushed me

[@Vsauce2]

Yeah, this one seems to have a happy ending until it... doesn't. Somehow a terrible story managed to get even worse.

[@vigilantcosmicpenguin8721]

Nobody won.

[@vibaj16]

I somehow misread "released" as "arrested", so you can imagine how I initially reacted to your comment

[@germanycountryhuman2227]

same bro

[@mr.boomguy]

I honestly don't blame her for dying the way she did. She was fighting a whole country. I cannot imagine the amount of stress and turmoil she must've been through...

[@davimelo9181]

As a lawyer myself, I'm constantly baffled with how emotional and irrational is the distribution of value among the evidence

[@psychopompous489]

People

[@roseCatcher_]

If you are a lawyer, that means you are sometimes paid to deliberately tilt that balance and take advantage of irrationality of the jury, the biases in their collective consensus. Necessary evil, but I don't consider lawyers human.

[@davimelo9181]

@@roseCatcher_ I see what you mean. Indeed, part of a lawyer's job is to create a narrative that emphasizes the evidence favourable to them. But that's done with the evidence that's given to them, that's already been made by the state. Moreover, a lawyer doesn't have control over the result of an evidence they introduce to the case (it can end up being prejudicial to the defence). So, yeah, you work with what you're given But more importantly, a lawyer works against abuses that can and often are committed by the state itself against the individual who's being prosecuted. An individual is always smaller and weaker than the state, and will always be ran over if there's the opportunity. So I'd say that's the real value of a lawyer's job, and I believe anyone who's suffered abuse from authorities will agree.

[@Vsauce2]

The human condition is the human conundrum.

[@Greywander87]

@@roseCatcher_ This is unfair. There's a lot of scummy lawyers, to be sure, but the entire idea is that both lawyers argue their position as best they can, and whichever one has the Truth on their side will be victorious. You can't have a fair trial if both lawyers aren't doing their darnedest to argue their positions. Even a guilty person deserves a fair trial, because we want to be absolutely certain that they were, in fact, guilty. A prosecutor and defense attorney arguing their positions are like a hammer and anvil striking together. If both sides argue perfectly, then all untruth will be obliterated between these two forces, leaving the Truth apparent to all. Sadly, they're not perfect, but it's the best we've got right now.

[@TheTrevorS1]

As an engineer, I feel the need to learn from the failures of math from real world cases like this one so I don't have to experience them personal. This video is well done.

[@raspxaseron6464]

KZbin makes no sense. They demonitize this and yet the multitude of things they should, such as naked yoga which I didn't know was a thing until Reddit pointed it out, they cast a blind eye to. I know losing the revenue from this hurts, but for what it's worth this was great and a interesting presentation. I always love to a new video from you in my subscriptions. To you and the team that makes these videos possible keep up the amazing work.

[@paulthompson9668]

RaspX Aseron It was demonetized because the video was not inclusive or diverse enough.

[@raspxaseron6464]

@@paulthompson9668 Thank you for the information. That at least sheds some light to the matter.

[@jerecakes1]

@@paulthompson9668 huh didnt know that can strip off monetization lmao wtf

[@paulthompson9668]

​@@jerecakes1 My comment was (somewhat) tongue in cheek. Sergey Brin and Susan Wojcicki (the people who control KZbin) have taken the approach that you're immunized from demonetization if you tow the party line (i.e., what Big Tech, Hollywood, and the mainstream media present as the "right" way to think).

[@sudonim7367]

@@paulthompson9668 Blind leading the blind right here

[@whatever56567]

This was a great video. The thing that was most infuriating to me is the fact that he didn’t do the obvious thing and weigh double SIDS vs Double infanticide (even with his poor calculations). Like how tf do you not calculate the rate of the accused crime alongside it if for no other reason than a control number to weigh your odds against when adding up the double SIDS likelihood? I do understand that the numbers are just that, numbers, and choices can negate that. But if you’re going to use the likelihood of two infants dying as ammunition and it has no meaningful contrast, it was just basically manipulating the court. Whether or not it was intentional. Poor woman, she went through hell.

[@EebstertheGreat]

It's the equivalent of arresting someone because they fit the profile of a crime, then arguing that only a tiny fraction of people fit the profile, so he is overwhelmingly likely to be guilty. Prosecutors do this so often, it is called the "prosecutor's fallacy." The most egregious example of this I have seen is _People v. Collins._

[@user-db3xu1hw7r]

man with lab coat say big number that's all it took

[@user-vn7ce5ig1z]

The even more obvious thing is to consider the countless other and more likely possibilities from genetic abnormalities to environmental hazards. 🤦

[@EebstertheGreat]

@@user-vn7ce5ig1z Right. From a statistical perspective, this is just the wrong question. If the only information we have is that somewhere there is a woman two of whose children died in infancy for unknown reasons, the question should not be "how often does that happen?" but "out of all times that happens, how often is it because the mother murdered them?" You can't just say a big number and think that means anything. You have to compare two possibilities: guilt and innocence. So if there are more cases of two children of the same mother dying from SIDS or whatever than from two separate murders, we should conclude the mother is probably innocent. And even if the former is much less likely, unless it is _overwhelmingly_ less likely than infanticide, the jury still should find her not guilty. There is also the separate problem of multiplying together two probabilities that have not been demonstrated to be independent. In fact, we have very good (and I think fairly obvious) reasons to believe they are not even close to being independent. Though, this is all a bit silly, because that wasn't the only evidence presented at the trial. The jury should really weigh all the evidence. Because this statistical argument is so much more prejudicial than probative, it never should have been allowed in the first place. This is ultimately how the appeals court ruled.

[@dragonkyng]

I mean it’s stated in the video the second kid received special monitors, so the hospital already showed that a SECOND SIDS related death was much more likely and felt it important enough to provide a system to help ensure their baby lived. It unfortunately wasn’t recorded properly, but I think that should skew the odds a massive amount

[@Crypt4l]

Even if his math was right, an event that occurs about every century, is sill a event, that can be expected to occur every century and not prove of murder.

[@roseCatcher_]

Nah it will be outside realistic boundaries if his calculations were correct.

[@Vsauce2]

SOMEONE'S gotta be the 1 in "1 in a something."

[@ZentaBon]

@@roseCatcher_ is it truly? Do you truly want to chance people's lives that way? Imagine this as a lottery to win, except you only win life in prison.

[@vigilantcosmicpenguin8721]

If seven million people buy a lottery ticket, one of them has to win.

[@Crypt4l]

@@vigilantcosmicpenguin8721 No, the chance to win the lottery is about 1 in 14 million, but your sentiment is correct :)

[@ShouVertica]

It seems crazy that someone just looks at a SIDS death and goes "yep, no way it could happen twice!" lol. What. This guy was insane.

[@alexeykozyrev5939]

This is a brilliant video. How could it be demonetized?! This is probably the most important work you’ve done on KZbin. Keep going Kevin

[@Lawh]

I have had this personal joke that I say to myself in my head, where when I have anxiety about dying or something, I think, "What are the odds of me dying when I randomly get a jolt of fear of dying?". I laugh, because I at the same time knew that it doesn't work that way, and how that thought still and joke still comforts me a little. This perfectly summarized what I never actually articulated to myself. Knowledge is power, and too little knowledge is misguided power.

[@Vsauce2]

Diffusing internal tension with a statistics/probability joke is amazing.

[@PtylerBeats]

This kind of reminds me of when I was a kid learning about religion. I always had these super weird questions for my dad and people at my church because things just didn’t make sense to me. The pastor said something along the lines of, “the second coming of Christ will never happen when you expect it. It wouldn’t be possible to predict when it’ll happen.” I dont remember the exact words, but I held onto that sentiment. Because it baffled me. Sooo… it’s not happening tomorrow because I could predict that it would happen tomorrow. And it’s not happening within the next 1 million years because I could predict right now that it’ll happen in the next 1 million years. Even though I knew that that’s not how predictions worked, part of me felt like his paradoxical statement implied that I could control when the second coming of Christ would happen because I COULDN’T predict it. So if I predicted every day that it would happen tomorrow, I would always be wrong, and I would forever have control over that. Because I could count on me being wrong.

[@alpheusmadsen8485]

@@PtylerBeats That reasoning even has a name for it, but I can't remember it off the top of my head (it may be something like the "prisoner's paradox", because it involves a prisoner deciding he won't be executed, because the judge said he'll be executed this week, but he won't know the day). As a religious person, I've never really been bothered by this, because I figure I'll just do my best to be ready for it today, and if it comes today, I'll be as prepared as I could be (give or take a bit of variation). Also, whenever a new date gets put on a billboard, or gets blasted in headlines, I always ignore it, because we're specifically *warned* we won't know the date, so anyone telling us otherwise doesn't know what they are talking about!

[@bengriffiths9631]

It always amazes me that some experts in different fields rarely explore ideas from outside their area. There was a flurry of papers released in medical journals fairly recently claiming to have developed a new analytical technique for reading a patients data. Turns out the authors had re-discovered numerical integration, a very basic analytical method in maths.

[@bjmben88]

If I remember correctly it was just the one author that made that claim, and they were quickly ridiculed and debunked in response papers.

[@micahphilson]

"This will revolutionize medicine as we know it! We call it... Calculus!"

[@penitentman7139]

Experts like to stay blind to anything that isn't their own way of thinking because, well they are the "expert" after all. All they care about is their paycheck, if what they're expected to do requires actual work, they just revert back to their closed minded, quick and easy solutions instead of taking the real life happenings for each individual case into consideration

[@Jvk1166z]

i mean, its not surprising to me. to be a medical doctor you dont need to have much statistical math knowledge as far as i know. if you dont have an interest in it personally, you're not gonna go research it. like if i have an interest in astronomy, im not gonna go researching medicine because thats not what im interested in

[@BertiferousRex]

There was an article about midichlorians that got published in a medical journal just to see if it could. It was.

[@gustavosaddi]

This is undoubtedly your best video so far! It’s great to watch the explanations of paradoxes e statistical probabilities. But seeing a real example of how a misinterpretation of a simple theory ruined somebody’s life is mind blowing. Please, keep up the series!

[@iluxa-4000]

1 in 73 million is not even that impossible, why did they go so hard on this?

[@kart182]

You serious?

[@iluxa-4000]

@@kart182 there are billions of humans doing things every single second, there are quadrillions small things that shift and change around us all the time. To get my point across clearer - the odds are somewhat similar to winning a lottery. Except you don't buy 1, 2 or even 10 tickets. Everybody buys hundreds, thousands of tickets every day. If anything, it's pretty wild that stuff like that doesn't happen more often. Now, of course, the math used to get to 1 in 73 million was *so* wrong, the situation itself is not a simple chance game, but still, it is not that unlikely that it would happen to someone

[@kart182]

@@iluxa-4000 I guess it’s subjective, so there’s no right answer, but I think your decision of what is improbable vs not improbably is kind of dumb. Yes of course, some odds are insanely tiny, like a human cell being found on Jupiter, 1 in a googolplex or something, but how tf is that relevant to real world probabilities? The probabilities of many things happening to and within the human population is not likely to be on a scale even remotely close to 1/googolplex, but much closer to 1 in 75 million. Many things we encounter every day have much higher odds than that. The odds of being struck by lightning in the US is around 1/1.2million, and you’re saying 1/73m is “not that improbable”. BRUH

[@jakey1995abc]

Am I the only one who thought this was common sense in the medical field... When something occurs once it tends to be much more likely to reoccur?

[@SoulDelSol]

Exactly

[@Vsauce2]

It hurts to even think about how obvious that should've been.

[@kennethkho7165]

Exactly

[@harischastoukis8471]

@@Vsauce2 I am a bit late to the party but even if the propability is 1 in 73 million you have 330 million Americans so a court should atleast face around 5 cases of this level of improbability. If my math is right the propability of having atleast 1 american this happens too is 99%

[@ernimuja6991]

Common sense works like that but that's a fallacy all on its own. Like if I get heads 50 times in a row, the next one HAS to be heads right? No. So the probability that the death of the second child is predicated on the first is also really low.

[@ehrichweiss]

In less than 2 weeks of September of 2019 I had my car hit THREE times. My insurance company(Progressive) didn't even bat an eye when I told them because I've had so many cars hit just in front of my house that they're used to it. Hell, I've been hit twice in a month's time more than three times that I can recall. It happens because my town is utterly full of people who can't drive, won't look when changing lanes, etc. and far too many of those accidents were hit and runs because they also seem to be drunk when they hit you(and a H&R charge is easier to deal with than a DUI so they will always run). For the record, I keep full coverage on my cars because of the hit and runs.

[@Vsauce2]

Ok, that's wild. And it sounds frustrating. But it's a good example of what's in this video!

[@Doppio3006]

I am an applied statistics graduate, and I have been telling students even way back, that statistics is one of the most important things to learn, and they just laughed at me. Thank you, Kevin, for sharing this video, even if KZbin demonetized this, we really appreciate this, keep it up!

[@RennyNanaya]

I love this somber tone integrated into the enthusiastic and curious framing. You really pulled it off well!

[@leidecarvalhodemello4594]

Just hearing about this makes my blood boil, when statics are used in court, there should be at least one highly educated matematician to check for these kind of mistakes, one life was lost, such a tragedie…

[@NaoyaYami]

But no one wants to pay math budget.

[@heyyou9137]

More idiotic is that later they found medical documents showing bacteria infection. Where were they when court found her guilty?

[@NaoyaYami]

@@heyyou9137 Possibly obfuscated so that it wouldn't influence the judgement.

[@navinsingh1730]

The doctor was doing the math, what else do you expect?

[@vibaj16]

or there should be more motion in court

[@RGC_animation]

For those who didn't get the "Two bombs on a plane is unlikely" joke, it's as likely as another person has a bomb in this circumstance because the first bomb is already guarantied to be on the plane.

[@morfeusfs]

But this is not so much about conditional probability, as he says in the video, but more about the Gambler's fallacy, right? The two events are unrelated, so one doesn't influence the other.

[@Vsauce2]

Right -- and you bringing one on the plane (or not) is entirely independent of whether someone else will. Conflating your actions with independent actions matters here.

[@Robbedem]

actually I'ld even dare say that if you are able to bring a bomb on the plane, the chance of someone else doing so is higher because it means there is very little security checking going on. ;)

[@RGC_animation]

@@Robbedem Haha lol that is true.

[@picklenik9658]

@@Robbedem Now that is what we call some sensible statistics, using some outside logic in order to better evaluate probability.

[@GoldeeLoxs]

I’ve been watching you and vsauce 1 & 3 for about a decade now and your videos have been awesome, educational, and entertaining!!! I’m so sorry that you got demonetized. It’s rough seeing content creators who put so much hard work and thought into their videos not get paid for their work. I hope you know that you, Michael, and Jake have made content that’s had a real impact on people all over the world (myself included). It’s not money and it won’t pay your bills, but I still would like to say: Thanks man!

[@Alkis05]

My statistics professor made all his exams with questions with high stakes like that: "Do you convict this person of murder based on this probability argument? Why?" or; "The probability of a ship passing near this desert island is X/week. How long do you have to make your poor rations last so it will last until the next one shows up" It was very tense.

[@alkatron768]

Another thought, both kids dying of that specific illness might be 1/73 million, what are the chances of both kids dying of any 2 unrelated illnesses? like 1/10'000? what about both kids dying of the same illness, but the illness isn't specified? that might drop the number to more reasonable 1/1 million maybe. I don't know if I'm on a wrong logic train here, but it seems somewhat relevant. That specific case may have been unlikely, but there are other unlikely cases that could also have happened.

[@CouchPotator]

That is indeed the point, you are on the correct train. The second kid even died of a bacterial infection, a fact that was somehow lost in the first trial.

[@willguggn2]

I don't get how it got through. Like nobody had ever heard of a family tragically losing two children before, because each specific case is almost impossible.

[@ZentaBon]

And what's sad is...just because it's unlikely to happen doesn't mean it didn't. :( we can't just go with what's most likely every time because many, many of our conclusions would then be untrue.

[@NaoyaYami]

That's exactly what that example of 2 car crashes in 2 months was about. That ex-expert treated both cases as identical which was obviously idiotic, since there's no chance that circumstances were exactly the same, especially since the parents already experienced sid before. Just another case of emotions (mostly pride I guess) triumphing over empyrical evidence and logic.

[@NaoyaYami]

@@willguggn2 Emotions. Just that. Most adults have this weird idea that children's life is sacred and holy but never even try to expand it to other adults. Hence, when 2 babies died under care of the same couple, humans wanted to see an easy to accept explanation and maybe get a feeling that the world will be a better place once the mother is sentenced. I guess that's similar to how ancient civilizations imagined all those different gods (like egyptian god Ra moving the Sun on the sky which we know is factually not true).

[@teabagfc]

An excellent video! In the first year of my maths degree I sat an Introduction to Statistics course in which the lecturer constantly used the Sally Clark case in his examples about probabilities and conditional probabilities, almost to the point that the students were sick of hearing about it. Nevertheless, there's a class of students who will *never* allow themselves to make mistakes on conditional probabilities.

[@Vsauce2]

That's great, Dom -- and it's a lesson that probably can't be reinforced too often.

[@Indrid-Cold]

@@Vsauce2 THE ONLY TRULY IMPORTANT QUESTION HERE, IS: What the FVCK was some nerdy statistician doing on the stand three years prior to THE CORONER/Pathologist, with the results of the goddamned autopsy?!? Anyone have an answer for this? How, and why did it take three years to find out that the CAUSE OF DEATH was a bacterial infection??? I suppose that’s too much to ask from a country where attorneys dress like penguins, and the judges still wear powdered wigs 🙄

[@th3n3wk1dd]

Great job Kevin. Brought a tear to my eyes but as an analyst, I have tried explaining this to many people and they never got it. Maybe it is my fault for not being able to explain it properly, but this video did a great job. Thank you.

[@angelicaleder]

Same thing happened in Australia in 2003 to a mom who had 4 kids die of SIDS (now thought to be due to a genetic mutation predisposing them to sudden cardiac death), she was imprisoned for 20 years and only had her conviction overturned and got out last year. Such a sad story, poor woman lost all her babies and then her husband even turned on her as well. Her name is Kathleen folbigg.

[@bentaylor8299]

4:28 P(A|B) isnt the probability of A then B. Its the probaility of A given B. With a coin flip, the probabily of A being heads given B is heads is 0.5, as its independent. But the probabilty of B being heads then A being heads is 0.25, as we need to depend on B also being heads. When with A given B we have assumed B is already heads.

[@fetchstixRHD]

Wanted to say that - while I know what was meant, the wording used is likely to be confusing.

[@cobalt7678]

Yup exactly

[@CheshyrCatt]

Thank you - I felt like I was being really anal when he was describing this.

[@lukasvik4636]

No I wasnt stuck on questioning my probability knowlage for like 10 minutes or if I just misunderstood or what was happening. And I was definitely not excited to notice this comment after asking myself if noone caught the mistake, especially cause it would not work with the joke in the end. So Thank u for saving my soul and mind 😅

[@bentaylor8299]

@@lukasvik4636 haha no worries. I remember making this comment, and it was an inconsequential thing but it kept playing on my mind

[@strawberryowl962]

It's like someone making a three-pointer basketball shot alone while facing backwards and then this one popular kid called it fake (even tho it has happened before) and gets bullied by the whole school for being a "liar".

[@chuck_norris]

lmao

[@ioannisloukas4131]

Is it a personal experience of yours?

[@noahsan92]

@@ioannisloukas4131 sounds like it

[@strawberryowl962]

@@ioannisloukas4131 Not the basketball part (I never played basketball) but the school bullying part since I get teased in my classmates a lot when I was younger.

[@iShionSinX]

True story, I witnessed another kid from my 4th grade class do it.

[@xenosbreed]

Amazing video, actually had me tearing up by the end, no wait its full blown crying. This is why I love science, sociology, and psychology so much, the intersection in how these worlds collide is so amazing, it effects our every day lives in mundane ways... but also in horrifically tragic ways.

[@Aglaesia]

Thank you for bringing light to such a tragic situation, and how important details are when people's lives are at stake

[@philrobson7976]

Wow, Kevin, you really outdid yourself in this episode. A sad and tragic outcome that I hope will correct some legal injustices. Keep it up!

[@Vsauce2]

Thanks, Phil! More on the way...

[@ZentaBon]

@@Vsauce2 that's good to hear. I hope you enjoy making these as much as I enjoy learning about these cases. It's tragic, as this sort of thing could happen to you, or to me. I can't imagine how truly terrifying it is to be in the situation she is in. I've had to stay away from true crime because it upsets me how certain people portray themselves over outcomes that, to me don't at all appear certain.

[@makfrags14]

I'm convinced vsauce is my maths and science teacher

[@DefnitelyNotFred]

Now we just need to call Kevin Dad

[@jack_of_all___]

And philosophy

[@Q--_--90909]

Math*

[@Thiago100Zwetsch]

Out of every video I ever watched on this channel, this, by no coparisson, is the number one. This is a masterpiece. Great job, Kevin. KEEP ON!

[@ZacJelke]

It is absolutely shameful that KZbin would demonetize this. I enjoy all of your videos but it is really interesting to see more real-life applications of the theoretical probability stuff you show. Fantastic video!

[@Hartbreak1]

Amazing episode. I wouldn’t be surprised in this case if that Meadow guy was already prejudiced when providing testimony and just chose the math that made her look the worst.

[@Vsauce2]

There's some odd evidence that suggests Meadow defaulted to guilt, including his ex-wife saying he assumed that child abuse was happening way too often.

[@lafcursiax]

Thank you for covering this tragedy. I wasn't familiar with this case, but having read about the satanic panic of the '80s & '90s, I'm all too familiar with how easy it is for flawed science to seem convincing when accusers have the specter of child endangerment to silence critical thinking. And of course, this terrible episode is a powerful argument for making sure everyone is trained in mathematical literacy!

[@Vsauce2]

The cult/Satanic panic especially in California is a shocking subject -- a documentary that Sean Penn narrated does a great job with it. It's called "Witch Hunt" and it's awesome. Check it out if you haven't seen it!

[@johncasebeer179]

Always love your stuff, but a practical discussion like this one is very much appreciated.

[@ZunarZulfiqar]

Kevin, well done. As Jake put it, a unique delivery method. This was heartbreaking, but seriously insightful. I don't get math, but somehow this just made sense and it was informative as I hadn't heard about this story before. Entertainment backed with a serious level of lessons to learn. I'm voting you do more of these.

[@noelblack8159]

Two Vsauce‘s in one day? It’s a Beautiful day for sure!

[@austinevans]

Terrific video my friend!!

[@PashtunChad]

never expected to see Austin Evans in this comment section. How does your comment have only 77 likes?

[@andreahaspeklova7093]

Could you make this a series? I don't know if there are any other stories with real life math failures, but still it'd be great. Anyway, I loved this video. Great concept, great work.

[@SamEy3Am]

I just wanted to drop by and personally thank you for challenging the way that I think. I have previously been brought to the brink of anger by your videos, but only because I wasn't willing to challenge what my own instincts were telling me HAD to be true. This video did not do that with me, since watching previously has opened my mind to thinking critically and in a way that mirrors reality. Keep up the amazing work! I know I deeply appreciate it. TL;DR - Thanks Kevin! 😀

[@AceMoonshot]

Kent Brockman: Mr. Simpson, how do you respond to the charge that petty vandalism such as graffiti is down 80% while heavy sack beatings are up a shocking 900%? Homer: Oh, people can come up with statistics to prove anything, Kent. 40% of all people know that.

[@kilangalangamoekalon]

Lisa: Dad, don't you see you're abusing your power like old vgilantes? I mean, if you're the police, who will police the police? Homer: I don't know, postguard?

[@lystalan]

Thank you for this video. I’ll be sharing with my engineering team. It is important to remember that when dealing with numbers and probabilities what we are really doing is trying to protect people from harm. This is an example of why it is important to think critical and not just go through the motions.

[@lucusloc]

It's also important to remember, especially for engineers, that statistics is really just covering for unknowns. As soon as you figure out those unknowns it is no longer a statistical calculation, but a deterministic one. That is what a huge part of engineering is; trying to convert statistical calculations to deterministic ones.

[@Vsauce2]

Engineering is a great field to recognize that we have known knowns, known unknowns, unknown unknowns... and values attached to all of them. 10/10 comment, thank youuuu

[@josealejandrorodriguez3818]

A wonderful video that brought tears to my eyes as a math teacher. Thank you so much for this

[@ItsShatter]

This video and your work on it deserves to be recognized, not demonetized.

[@RLeaguer_Saint]

Beautifully and compassionately presented. Willful Ignorance of science has never been more problematic as it today, and this is a great example of the consequences. Thank you.

[@Vsauce2]

Thanks, Saint -- one of the most glaring elements to this story was how indignant Roy Meadow was about his ignorance of the principles at work. Really, really bizarre.

[@TheSykobanana]

Mate, that was incredible and being in Australia, I had no knowledge of it at all. Thankyou for making this!

[@Vsauce2]

Thanks, Syko -- Australia's got some pretty crazy cases like this, too. Might poke around a bit to see if there's a good math-related topic on the island. :)

[@camerongordon5879]

This is so sad. I can't imagine what it would be like to go through something like that. Thanks for the educational insight.

[@TheMor3epic]

Such an amazing video, thank you Kevin for all the work you put into these videos.

[@EebstertheGreat]

The prosecutor's fallacy isn't about erroneously assuming statistical independence. It's about falsely conflating the p-value of a test with the probability that the defendant is innocent. It's possible to perform the test correctly and still be guilty of the fallacy.

[@UsmanMuhammadNooruddin]

This is a very good and a very deep explanation of the fallacy that clears a lot for me. Thanks!

[@EagleDarkX]

I think the best example of it - when talking about improbable, recent events - is the moderators' and internet's response to the Dream cheating scandal. Statistics is a terribly misused tool.

[@mufflebuns6322]

@@EagleDarkX Oh, with statements like the 1 in 7.5 trillion chance being spread around, rather than the more accurate version of it? (I haven't taken Stats in a while, but I think it was more so like 1 in 7.5 trillion similar simulations would produce such a result)

[@EagleDarkX]

@@mufflebuns6322 The point is not that the 1 in 7.5 trillion is inaccurate, it's that nobody understood what that number represents. What that number represents is the likelyhood that the underlying probabilities are as defined in the games code are, correctly, used to determine the outcomes of both ender pearls and blaze rods. Some people took it as the chance that dream's runs were not cheated. There's a nuance difference there, a step that if it weren't skipped, would have saved us a whole lot of drama.

[@ZentaBon]

@@EagleDarkX can someone explain this? Did he cheat simply because of the rarity of what happened?

[@kayoliver5530]

Thank you so much for doing this video, I remember this case so clearly and the hate mob that were screaming and shouting "murderer" at the prison van she was in. I could never even imagine the pain Sally and her husband went through, still to this day there are so many people who staunchly believe she is guilty and will not let her rest in peace or her husband and child live their lives as best they can. Roy Meadows should have been given a life sentence. I hope more people here in the UK see this video.

[@mattrenegar476]

Total BS that this video got demonetized. SHAME ON KZbin for not reversing the decision immediately. You are awesome Kevin. Please don't let this hold you back from producing the amazing content that you always have!!

[@adnanelouadghiri6880]

Your videos are always getting better to the point where you can't decide which is the best one❤️ good job!❤️

[@albl247]

This may be one of the most important videos you have ever done. Thank you.

[@Vsauce2]

Thanks, Bisley -- it certainly felt that way making it.

[@Bomkanon]

This was honestly incredible. Love the new format. Would love to see more like this in the future!

[@Vsauce2]

Thanks, Jacob! Perhaps you will...

[@vez3834]

@@Vsauce2 Eh, what are the chances?

[@brandonpettit8165]

Interesting to see the effects that one person can have in the court room. Appreciate everything that you do for creative educational math videos

[@pippyharrison9745]

We used this as a case study in my stats degree as an example of misconceptions in decision theory. Amazing video

[@Skyhigh91100]

I’ll be honest, I had my doubts about the video living up to the pre-release hype, but damn if you guys didn’t deliver something really special here. I’d go so far as to say this is a real level up for the channel. Not that every video needs to be like this going forward, but I would really love to see more of these grounded, real life examples of some of the concepts (probability especially) explored in previous videos.

[@justaregularguy3071]

I was so hyped with the promo you showed yesterday!! Watching it right now

[@RealCosmosry]

Great work Kevin! We need more of such videos, this was so insightful and engaging.

[@LucasMartins-gs6fd]

Kevin, this was a great video. I am moved in ways I did not expect. Thank you

[@richardfrenette6648]

Wow, amazing video Kevin. Great story, great perspective! We want more of that. Medical, engineering, financial (2008 debacle), math errors are important to understand.

[@Vsauce2]

The math of the 2008 financial crisis probably would not fit in KZbin's 10-hour video limit.

[@khianjoshabesamis9608]

THIS IS AMAZING. The ingenuity, the education merging with the thrill and drama. OUTSTANDING

[@Vsauce2]

That means a lot, Khian -- THANK YOU. SERIOUSLY.

[@khianjoshabesamis9608]

@@Vsauce2 First time I actually got a reply from a KZbin celebrity. That reply just made my entire week a whole lot better. Thank you for that too

[@sumitbajpai3126]

Incredible video!! Best work of you till date. Absolutely amazing

[@sandraviknander7898]

Powerful video Kevin! This is the sort of trails you would read about in one Kafka books. This is also the reason all lawyers and judges should have training in statistics.

[@BrickTsar]

Excellent video Kevin. This is so important to understand. Thanks for making this. People just don’t get it most of the time

[@stridersoa]

Powerful stuff dude! Thanks for consistently providing amazing content and expanding a love of knowledge and math!

[@Vsauce2]

Thanks, Delaron :) There's more in the pipeline!

[@gauravrana7478]

Really liked this series/concept. Expecting more videos like this one.

[@stargazingsongs]

if you flip a coin 99 times and it lands on head every single time, the chance of it landing on heads the 100th time you flip it is still 50%

[@tatianemarques6002]

Man, this is the best KZbin video that I seen in years! KZbin just increase the probability for more views 😂😂Go, go Kumon!! Good job!

[@slevinchannel7589]

@HคMMคď MцʂŤคϝค Youre a science-fan, yes?

[@sugibudder]

9:35 My first thought was to consider how many times she has tried, its not suprising to win a 1 in a million game if you try it a million times.

[@ottlight]

you still only have a 62% chance

[@sugibudder]

@@ottlight My point was that we automatically ignore all the fails because of confimation bias.

[@dustin4575]

Great video! Thank you for sharing a piece of this tragic story.

[@holymackerel]

Wow. Amazing video and story! Fantastic presentation, as always!

[@geoffist]

this makes your already amazing videos even more practical. love it. keep this up!

[@Vsauce2]

Thank youuuu, lastoneout! Keep an eye out for more. :)

[@adamnorthrop79]

Can’t believe KZbin demonetized this! It’s educational and entertaining. Nothing about this goes against their guidelines.

[@r.ferguson486]

Wow, what a phenomenal video! Thank you for making this ❤️

[@andrewsammons9643]

I knew this video would be upsetting and difficult I did not imagine how awful the reality of what actually happened would be. Thank you for making this video.

[@Paladaino]

Thank you Kevin. I missed this type of videos from you. You are an xcellent storyteller, I wish to see more of this content. Cheers.

[@Vsauce2]

Thank you, Pala :) The story videos are the hardest to make, but they're the most fulfilling.

[@ShayanSaqiba]

the editing is so cool i love it definitely bring him back

[@Vsauce2]

John Swan nailed it on this one.

[@miguelcordova4137]

you are doing great bro love your videos keep going, I'm impress of how well you have improve since the first time i found u in yt

[@mihaihuidan573]

How could someone demonetize this? This is one of the most interesting videos on the whole youtube.