Does math belong in the courtroom?

[@Gabriel-um9hm]

I once got a speeding ticket after a car passed me. In court the cop admitted that my car was over 200m away and the beam on the radar was 30 degrees wide but claimed that the radar was pointed right at me and he's sure he didn't accidentally get it on the car that passed me. I pointed out that a 30 degree beam at over 200m is over 100m wide which is over ten times the width of the highway and would of reflected off both cars. The prosecution then said that math is nothing but conjecture and I was found guilty on a 30 over ticket despite doing the speed limit. We need more math in the courtroom but we also need better educated judges.

[@robertgomez5378]

Perhaps a court math expert to testify on the legitimacy of math.

[@huge_letters]

@@robertgomez5378 well that's why usually experts on all kinds of studies are welcomed into to court to give insight on intricacies of life. Howefer math mentioned in OP is very basic and any person who finished high school should be able to deal with such problems which only goes to show how educated this judge was.

[@undeadman7676]

This is why terrorists exist

[@Hi_Brien]

@jocaguz18 I know lawyer pretty well who wouldn't be able to do that calculation. They didn't do particularly well with maths in highschool, and that flaw in their learning carried into university as well. A lot of folks concerned with law aren't concerned with mathematics, so I don't think it's fair to be too surprised that there is a judge somewhere in the world that tries to avoid using math especially on lesser crimes like that.

[@undeadman7676]

@@Hi_Brien There is a world of difference between ignoring incredibly complicated multivariable statistics and ignoring the basics of trigonometry. The Law of Sines has been around since the 1700's. It's incredibly easy to use. If any judge ignores evidence based on basic laws of math, especially when that evidence completely exonerates somebody, or at the very least explicitly outlines reasonable doubt, that judge should immediately be fired. Period. Stop defending morons. It makes you one too.

[@nxtech201]

"Have you ever met people? " that hit extra hard.

[@sohn7767]

Not since the quarantine

[@gordontang7837]

Didn't see that one coming

[@Galatzo]

404th like :(

[@nexovec]

hey, I just wanted to ask what is the outro music? This is here because I wanted you to see this.

[@jonathankrider6170]

it is quarintine... i have kind of forgot people exist

[@MK-13337]

"dear ladies and gentlemen of the jury, the probability you all were chosen to be in this jury is about 1 in ten googol. Therefore this jury isn't randomly chosen and we must declare a mistrial"

[@Vykk_Draygo]

But juries aren't random, and there is no requirement that they must be. Jury pools are somewhat randomized (seeing that they must be pulled from a certain geographical area), but the actual jury is most definitely not random, and is, in fact, carefully selected.

[@MK-13337]

@@Vykk_Draygo The jurors are randomly selected from the pool, and then both sides of the case can disqualify some jurors. So in truth I know my calculation is off. And people don't really know how random jury selection is. I don't want to do in depth research of the US legal system for a youtube comment joke 😉

[@TroyVan6654]

Except you ask the judge, not the jury, for a mistrial

[@daddylonglegspidersdontexi3210]

ladies and gentlemen the probability of the defendant being born is over 1 in a trilliom therefore they cannot exist, case closed

[@leotamer5]

@@daddylonglegspidersdontexi3210 The experimental probability is 1 in 1.

[@nommindymple6241]

“Million-to-one chances...crop up nine times out of ten.” -Terry Pratchett

[@valeweinmann9907]

It's always nice to find a terry pratchett quote

[@diribigal]

I think this is mathematically accurate for a population of around 2 302 586. For the population of the US, it's more like they crop up in the ballpark of 10^(143)-1 times out of 10^(143).

[@trumanhw]

@@diribigal no no, 330m i thought?

[@diribigal]

@@trumanhw yes, I used a US population number of around 330million to get my "one out of 10^(143)" chance that a "million to one" chance wouldn't occur

[@acekotana4425]

@@diribigal that's a big number that I'm too dumb to understand

[@alexanderkrizel6187]

Numbers don't lie. People misusing numbers do.

[@itachi6336]

Very true

[@pepepeepee5555]

People misusing number don't lie either. Lying is assuming a false statement intentionally, people misusing numbers do not lie.

[@joelmiller2601]

Missed opportunity bruh, keep it short and simple. “Numbers don’t lie, people do.”

[@alexanderkrizel6187]

There is such a thing as too simple. In your version, you cannot be sure if all people lie, some people or what the relationship is to numbers. Mine is pretty straight-forward. People who MIS-use numbers are lying, not the numbers themselves.

[@joelmiller2601]

Alexander Krizel Not really, its all about context, and I’d wager most people can tell. To me, yours just elaborates on what is already a given. Pretty much the same.

[@Sam_on_YouTube]

I have used math in the courtroom. You have to explain it REALLY well to the judge, jury, and other lawyers. Generally, if you can explain it visually with 1 page, that tends to help.

[@lightningstriking7]

@Roman Hauksson-Neill no! Now leave him alone...

[@hakor_]

@@lightningstriking7 chill

[@iwatchwithnoads7480]

@@lightningstriking7 well that's a lawyer alright. figures

[@user-jd1cy9gp3q]

Next video: Does math belong in the bedroom?

[@merug4349]

LMFAOAOAOA

[@JanneVirsunen]

In Swedish, the word for the number six and the word for sex is... sex.

[@michelbruns]

Janne Virsunen almost same in German Sex Sechs

[@_cynth_wave]

Always.

[@JanneVirsunen]

@@michelbruns Germanic languages unite!

[@bobthemagicmoose]

I was shocked in law school how mathematically disinclined most of my peers were. When discussing this topic it wasn't so much that our math intuition can be faulty but that math is some sort of sorcery that only wizards can practice. (and no joke, a student wanted to bring a calculator to a test because there would be a question with single-digit multiplication)

[@hanzeggers3576]

Scott Richards that could’ve also been because more Advanced calculators can be very easily used to cheat if Professors don’t know what they can do

[@matheny2014]

Arcane is the word you are looking for.

[@hanzeggers3576]

matheny2014 hahaha great one ☺️👌

[@johnherrera5261]

To be fair its pretty easy to trick someone using statistics especially if you hide the base numbers

[@life42theuniverse]

@Tucson Jim 8) from Caesar Augustus

[@upandatom]

I misread this as "Does math belong in the bedroom"

[@somerandomweeb4836]

1+1=3 Yes it does belong

[@zachstar]

There is a lot of potential for some good content with that title though.

[@gamepocalypsegaming278]

Well if you’re Rachel Riley, yes.

[@albertbatfinder5240]

Go forth and multiply.

[@pupperemeritus9189]

courting room instead of courtroom

[@SCP.343]

13:17 missed opportunity to say "that does not mean that Bob's your uncle.".

[@simonhallin8909]

Courtroom mathematicians: Of all 100 people we tested no one was born on January 1st, therefore we are 100% certain no one is born on that date! Ramanujan, Euler, Gauss: Are we a joke to you?

[@KnakuanaRka]

Yeah, someone doesn’t know their statistics.

[@m.caeben2578]

I love you included Ramanujan.

[@simonhallin8909]

@@m.caeben2578 Ofcourse, one of my favorite mathematicitons

[@ianmoseley9910]

All racehorses are deemed to be born on January the 1st

[@jeffreydenenberg7101]

Even as a high school junior it immediately seemed wrong to me when he said they multiplied all the p values

[@Elite7555]

Me also. The way they did it would suggest that changing your employer raises the probability to be a murderer, which obviously is nonsense.

[@AlcyonEldara]

Me too. Sample 1: 6 heads 4 tails Sample 2: 4 heads 6 tails Somehow ccombining the 2 should make it less likely? XD

[@danielgautreau161]

@@Elite7555 That is a perfect way to explain the fallacy in a non-technical way.

[@zenlizard1850]

"That's the third nurse in this video." Three nurses in one statistics video? what are the chances of that?

[@MultiPleaser]

"Not even 100 million nurses in the world". However, there are about 3 billion KZbinrs, so U would guess the odds are approximately 100%

[@laurendoe168]

We did this exercise in 5th grade. Sure enough, 30 classmates and there was a match. BUT... because we were all within one year of age, this meant the match was also born on the exact same day.

[@jdrissel]

I was thinking that everyone should have the right to a statistician in addition to an attorney.

[@kennethkho7165]

they already have the right to call statistics expert witness

[@mikeguitar9769]

100% of statisticians agree

[@linus6718]

@@mikeguitar9769 Haha

[@rogerdsouza4724]

Or should there be a court appointed statistician bound towards particular courthouse or even cases if their nature calls for it.

[@luketownsend5048]

“I dont think there is a right answer regarding how to use numbers in courts, besides use them correctly” aaaand subscribed.

[@WalterLiddy]

Yes, but often the lawyers actually DO understand the math, they just misrepresent it because they know it's easy to confuse a jury. So at best the opposing side gets an expert to explain that their 'evidence' is not legitimate, and for most jurors that's a wash, because they just see a he-said, she-said situation.

[@RC32Smiths01]

Math has quite a place in forensics and criminal justice purposes. I'd say it is very interesting to incorporate math into the law!

[@joelmiller2601]

Yes! That’s what immediately came to mind, especially in cases of forensic engineering where it needs to be determined why certain structures/products fail and whether it’s the fault of the design or because of poor maintenance.

[@RC32Smiths01]

@@joelmiller2601 That is very spot on!

[@91722854]

@@joelmiller2601 U study forensic engineering? Has it any relations with forensic psychology or criminology?

[@louf7178]

It, statistics, is used all the time with regard to DNA probability; it's usually like 1:3 trillion (?) match probability (of which virtually everyone is taking the professional's word for it).

[@evil001987]

For every physical evidence ever brought forward one could always make an argument that there is a false positive. Goes for DNA-matches, eye-witness accounts, etc. Without statistics and mathematics, forensics doesn't exists. If you ban statistics from court, you will need to ban forensics. Still we have people commenting that it doesn't have a place in court-rooms, as shown in comments in the video.

[@crystalwalker6496]

I remember an episode of a very old tv show, Maverick. So the title character is a gambler and knows stats a bit for his time. He is the only man on the jury who has doubts the accused committed murder. Maverick gets all but one of the jury to change their minds. With the last one, he makes a bet. If he can draw five pat hands from 25 random cards, the jury votes innocent. But if he can’t, they vote guilty. It looks to be a low probability, but actually there’s a high probability of getting the 5 pat hands.

[@moroni8299]

Was the show 12 angry men?

[@Chronischer_Innenbahn-Laeufer]

What are pat hands

[@jackiemowery5243]

@@Chronischer_Innenbahn-Laeufer if you are honestly asking; a pat hand in poker (the game in question) is a high value hand (high probability of winning) you would have confidence in without drawing replacement cards to improve your chances of winning. You would "stand pat".

[@Chronischer_Innenbahn-Laeufer]

@@jackiemowery5243 I know poker. I don’t know pat hands. Is it two of a kind? Thanks for answering by the way. Is it a special type of poker? I never heard of replacement cards.

[@jackiemowery5243]

@@Chronischer_Innenbahn-Laeufer That would be draw poker. You start with 5 cards dealed and you can discard up to 3 in hopes of improving your hand. A pat hand might mean you received a full house (3 of a kind and a pair) or a Royal Flush.

[@tylermacdermott5467]

I remember a case from more then a decade past. A man was charged with rape and murder because he had a key to the women's apartment and lived in the same complex. With no other evidence. It turned out that both his and her apartments could be unlocked with each other's keys. Since the keys had only 5 pins and each pin has only 5 cuts and the cuts between 2 adjacent pins can only vary by 3, then you factor in the number of apartments. Basically something that seemed very unlikely at the time of arrest, turned out to be quite likely. A sad story for everyone involved, but another example of statics in court.

[@MrsTrap99]

I like these types of videos where you explain how theoretical concepts apply to real life situations. Keep up the amazing work!

[@Pennycilin3]

"Events with really low probability happen all the time!" Gacha players: "Finally some motivation."

[@blob7800]

thanks

[@Nalianna]

Lloyd Christmas: "So you're saying there's a chance?"

[@utoothheartyeight]

"Nobody goes there anymore because it's now so crowded."

[@number1sleeper925]

So me getting Summer Kama can happen?

[@VRUmasterVRU]

A great way my maths teacher taught us the birthday paradox is this: What is the probability to fly on an airplane with a bomb. Let's say its 1 in 30 million. Now we can calculate the probability of flying on an airplane with two bombs: 1/30m^2 = 1 in 9 with 14 0's - that's quite the high number. Should we just carry a bomb ourselves for safety?

[@zergreenone8111]

I don't really think that is that related to the birthday paradox, I think it's more closely related to the gambler's fallacy

[@VRUmasterVRU]

ZerGreenOne You are correct, it’s not the same but has some similarities.

[@adrianalexandrov7730]

everyone who'd answered "yes" in my class would fail: it's independent events, so you bringing bomb does not affect probability of a terrorist bombing exactly that plane.

[@bug5654]

@@adrianalexandrov7730 Excuse me sir, this is my emotional support bomb, thank you VERY much. (Plz no nofly list me FBI).

[@epicm999]

@@bug5654 rip

[@isabella-nu2fc]

Math belongs everywhere

[@bulldozer8950]

As long as it’s correct math...

[@aleksszukovskis2074]

People who cant use it correctly do not .

[@91722854]

@@aleksszukovskis2074 Math belongs everywhere, just the people who are incapable of using it correctly don't belong anywhere

[@aleksszukovskis2074]

@@91722854 i agree

[@gasoline9666]

Math is everywhere, too

[@PapaFlammy69]

TL;DW: nah

[@Ennar]

Well, clearly you don't know anything about maths... Just joking, Jens, cheers!

[@dimitribonanni4035]

Too Long, didn’t wead?

[@strebicux6174]

Tldr*

[@d.l.7416]

@Strebicux TL;DW = too long didn’t watch Coz it’s a video✨

[@angelcaru]

@@dimitribonanni4035 Too Long Didn't Watch

[@heikanaomi4426]

I needed this video to check myself. I always try to see all sides before ever making a judgement (in my mind or out loud)..but I didn't realize I was still being duped by the misuse of the numbers. Thank you so much!

[@benwinstanleymusic]

your explanations are so clear and understandable, which is often really hard for something like stats. Keep up the great work Zach!

[@SCP.343]

One in a million, with more than seven billion people on this rock, doesn't really mean as much as it sounds like it means.

[@pwnzus]

The meaning wouldn't change though," one in a million" is still "one in a million" even if there were a trillion people on Earth.

[@jonathanshaw6784]

There’s a ted talk buy a woman involved in the spam filter for twitter. With that many tweets a one in a million chance happens several times per minute.

[@SCP.343]

@@pwnzus yes, it would be in the literal sense the same, each time you run an iteration of a system the odds of each possible outcome remains the same. But the more times you run it the more the actual occurrences of each possible outcome begins to look the same as the model of the statistical probability.

[@deanfarina8968]

@@pwnzus :What you said is true jm,but it dose increase the chances that the 'one' is standing right next to you...with a frozen banana in his left hand while standing on her right foot whistling Dixie and farting the star spangled banger in Portuguese and and and and...ok...I'm done...(Puts his helmet back on and wipes the drool from his chin as his Texes catheter gently overflows onto the counter of the Dairy Queen where he thinks he works as the attendants slowly unfold the straitjacket which happens to be just his size except for the strap that goes between his unequal legs which are the same in length but different in girth like this absurd diatribe you read to the end for no reason other than the fact that...wow...it sure is dark in here dot,dot,. Please ignor the name and picture above as that is not me...or any of us for that matter.

[@jmchez]

Are there seven billion people available in your list of suspects? 370 million in the USA, 8 million in New York City, 2 million in Manhattan and so it goes.

[@ptolemyhenson6838]

First video from this channel, coming from the other one. The contrast is insane.

[@concrete_dog]

Hey Legal Eagles! Today we'll be talking about math, and why lawyers hate it!

[@louf7178]

Don't be so quick to feel invincible - manipulation is their craft (which COULD right or wrong); I'm entirely perturbed of plain effort for winning, and this, sadly, is what is mostly strived for e.g. defense lawyer firm: who would hire a firm that has a losing record? - job security in spite of rightful justice.

[@tudornaconecinii3609]

Except that lawyers, unlike judges and prosecutors, do NOT have it as a fundamental professional standard to be truth seeking or objective. Their job is to present the strongest defense for their client, by any legal means necessary. This is a feature of the system, not a bug.

[@tudornaconecinii3609]

Hell, even if you look at the vows taken when entering every given judicial profession, this checks out. Lawyers are the only ones who do NOT have to swear on impartiality under oath.

[@concrete_dog]

What

[@abijo5052]

@@tudornaconecinii3609 exactly. Because that's the point of having a legal system of two lawyers. It reduces bias by enforcing bias. If a lawyer had to seek justice and impartiality, then their personal biases, such as what justice means to them, would affect the outcome of the case. Instead, both lawyers are given a strong reason to fully be biased towards their own side, so to try their hardest to win. So any ideas of justice or whatever they might have don't matter, as they just want to win the case. By using this, an impartial judge or jury (their bias is a different issue) can see which side has a more convincing argument, as any argument from one side will be fully dissected and argued against from the other side.

[@WheelDragon]

I feel like statistics is one of the best ways to avoid anecdotal evidence. If someone says "hey here's this one time where this happened" you can respond with, "yeah, but that thing was an anomaly, and is a cherry picked case."

[@MrMarclax]

but what about the times the statistically improbable does happen?

[@nedinnis6752]

@@MrMarclax It won't get much weight if you try to use it as evidence, as far as I know.

[@MrMarclax]

@@nedinnis6752 Im not saying that using something improbable as proof is valid. Of course it wont hold much weight. What I was insinuating is that, in a court of law, you can't counter someone's testimony because what happened to them is statistically improbable.

[@KevinFlores-ey8tz]

I'm thinking Scott Steiner might've did some wrong calculations when he said he had a 141 2/3% chance for winning at Sacrifice

[@strebicux6174]

You know the numbers.... And they spell DISASTER for yoy

[@apowergso]

0:56 my sister was born on January 1st! I predicted it when I was a child. I love when my predictions are correct

[@cawl8122]

I know this is dumb but there's a random blue pixel in the top left of ur black background and it's bugging me

[@hamiltonianpathondodecahed5236]

where exactly

[@progamming242]

It could be your screen

[@consumebee9540]

no I see it too

[@dercoder015]

@@consumebee9540 now what is the probability for you to see it too on your own screen?

[@fedem8229]

I also see it

[@nneichan9353]

I hope to never be on a jury again. I was the only health professional not discharged from the jury, simply because the judge felt the pool numbers were getting too low. He then told me that when the jury was deliberating I could not inject any opinion based on my experience even if I new a conclusion arrived at or stated by another jury member was wrong. I lost a significant degree of respect for the legal system that day.

[@Shiraori999]

"How can people be this stupid?" "Have you met people?"

[@cabooey2905]

your "This is How Easy It Is to Lie With Statistics" is one of my favorite vids because what it shows and how messed up things can be

[@peter1062]

Wouldn't the chances of matching DNA profiles increase dramatically if people were closely (or not so closely) related? Isn't the frequency of certain genetic characteristics higher in families or tribal communities? People in isolated areas like small islands have often been intermarried for many generations.

[@ChJuHu93]

Usually yes. I've not read into that test, but for full analysis of the genom you can even extract the biological relationship between the two.

[@krist264]

Really appreciate this channel breaking down fascinating concepts in understandable language to help people think more critically and perceive things from different perspectives.

[@happycamperds9917]

Lawyers: “We spent 8 years in law school and now we need to learn statistics too!”

[@ableone8956]

Yes you do!

[@sweepsweep5572]

doctors need it. merchants need it. everyone who wants to do better does.

[@taragnor]

Honestly I feel like everyone should learn statistics. Even for the common person, it'd solve a bunch of the confusion over interpreting coronavirus numbers. So many arguments are made using statistics and knowing how to interpret them is very important.

[@s6th795]

This was recommended right above your "how to lie with statistics" video. Very fitting.

[@Aedi]

The birthday problem is 100% a paradox. Paradoxes aren't just self contradictory statements, there's actually 3 types of paradox, one of which is any problem or question which has an extremely counterintuitive solution/outcome. The birthday problem is a paradox because it doesn't fit with how our base intuition works.

[@jay-xj1om]

Paradoxes _always_ stem from imperfect understanding of reality. If they seem counter-intuitive it's because our intuition was flawed to begin with (which it always is due to our rather poor sensory organs).

[@jp4431]

@@jay-xj1om kzbin.info/www/bejne/oXvdhK19l8uWZs0

[@huge_letters]

@@jp4431 Liar's paradox is not a paradox - when you make a statement you just leave out the first part where you also admit that this statement is true. Year is 365 days long = It is true that year is 365 days long. So if you boil it down to essentials statment "I am lying" is the same "It is true that this is a lie" which we can then boil down to saying "A is true and A is false"(A and not A). You can already see the problem here but to give an example - "This bottle is blue and this bottle is yellow". Nothing paradoxical about this - just semantics. I mean if there was a paradox which be just contradictory by it's nature - it's a pretty clear indication that it's actually our misunderstanding on our part since self-contradictory things cannot exist by definition.

[@DanteKG.]

If i remember correctly the very definition of a paradox is a contradicting statement. So yea, i would say that counter-intuitive statements don't qualify as paradoxes

[@danielgautreau161]

There are many math results that are traditionally called Paradox that seem counter-intuitive or seem at first glance to be wrong or because it's shown that something must be false by showing that it implies1=2. Russell's/ Simpson's/ Burali-Forti/Euler-Cramer/Tarski-Banach, etc. But whether a result gets called Paradox is a matter of taste.

[@TheAlison1456]

The most interesting thing you said in the whole video is something to the effect of us already making probabilistic inferences. That's taking a subject out of the cold, dead, deceivng hands of academicist white paper culture and showing the humanity it in fact has.

[@ChadDerekJacobson]

if there's one thing people don't understand more than exponential growth, it's statistics, and if there's one thing people don't understand more than statistics, it's probabilities my mind is CONVINCED 23 people is not enough for a birthday match after just comparing one person with 22 (instead of taking the next person and comparing by the next 21 and so on)

[@Ivana-xm4wi]

I think that a statistician or two should be present by the law at the trial if statistics is used, so that data can't be biased.

[@Jacob-ye7gu]

20:40 I dont know if you were doing this, but the way you said "even with ted bundy" reminds me of a fallacy we commonly see, which is conflating the severity of the crime with the likelihood of guilt - or similarly, the magnitude of the victims' / families' emotions with the validity of the evidence

[@Aruthicon]

Ah, yes, Januray, my favorite month next to Apple. I don’t know where I was going with that joke.

[@skfok8472]

R/iamveryrandom

[@strebicux6174]

@@skfok8472 r/foundthehondscivic

[@YouTubeallowedmynametobestolen]

I can't figure out where you went with that joke. But you got there in style, my friend.

[@bradenborman4396]

I try to keep up with your videos and a lot are just over my head, but they’re all enjoyable! I like this one the best

[@CrittingOut]

This is funny because i just recently rewatched your how to lie with statistics video

[@minimalistic_banhaus]

Can you imagine your only two children dieing of SIDS and then you are convicted of their murder?

[@Felixkeeg]

18:18 basically another case of "those fookin' biologists"

[@egpimp]

Speaking of math I remember this one problem I had on an assignment It was essentially this: You had 2 cops, both were about 10 miles away on the same road , were able to communicate with each other through radio, and the speed limit is 60mph. Cop 1, earlier in the road sees someone driving by, checks them with radar going exactly 60, all fine, but they're suspicious for some reason so they tell cop 2 about this car, start a timer, and wait. A little under 8 minutes later cop 2 sees the person driving by, checks their radar and still 60, but after doing some quick math (Math that if done right proves the person HAD to have gone over 60 at some point between the cops) and tickets/gives official warning for speeding. Although the cops never actually saw it, would they be justified in giving a speeding ticket to someone (So long as their math is correct in all aspects) for a speed limit that they were mathematically proven to have broken?

[@ntdscherer]

Assuming they actually measured the distance correctly, marked the times correctly, and did the math correctly, I don't see why not. The only possible issue is multiple cars matching the description, so they would need to do it by license plate number. That's how they ticket people using aircraft after all. There are markings on the highway, and they just use a stopwatch to see how long a car takes to get between two markings a known distance apart (one mile I assume). Then radio it to a car. In that case the car never passes out of view, but it's the same principle. What was the expected answer for the assignment?

[@rayanon]

Hey Zack, you really have a loooooootttt of information in Math, Physics, Chemistry and Bio. I watch your videos often to deeply understand certain concepts of the universe. Your level of education and academics must be really verry high. What degrees and education you have earned?

[@genericusername4206]

Sir Genius he is an engineer, he has a video on it

[@Fruitcake_4everzz]

This is the same thing is you having a dream about your aunt and finding out the next day your aunt died...it seems supernatural sure but you dream every single night, dreams populated by people in your life, and people die all the time...so it's actually quite probable that this happens all the time. Also when you think of numbers like 1 in 73 million, there are 6 billion people, so that's a lot of people that that happens too

[@joaoruiz2577]

Zach, do you know the book "Weapons of Math Destruction" by Cathy o'Neill? It's basically about the misuse of math in situations like loan applications, directed advertising and even job interviews! It goes in the same vein as this video, exposing how math can be used maliciously (actually, used only to increase profits, not bearing in mind anything else)

[@leehutchinson7005]

The key in the last case, which is simpler to understand, is that the wrong question was put forward in court. They asked the probability of a match and being innocent instead of the probability of having a match and being guilty. In the UK if the prob was 1 in a million for being innocent then the approx number of people who would match would be 60. So on stats alone the probability of being guilty is only 1 in 60.

[@Quadratical]

1:35 "Januray" JANURAY

[@diribigal]

To be fair, the chances of being born on Januray 1 are pretty low.

[@thepetrichor443]

i clicked on the video and was immediately sent back to my 2nd year of college when i took discrete math 2 and learned about the pigeonhole principle, which is basically that birthday example you went over

[@noddle045]

Comparing losing both your infant children with winning the lottery...yikes.

[@OnePieceFan4765]

One of the issues is they like to calculate probability for selection of a random person meeting certain traits but they didn’t pick a random person they convicted them BECAUSE they met the traits

[@mattschumacher4581]

This is the problem with the justice system. We assume that “highly likely” is the same as “definitely”. If we abide by the saying “guilty until proven innocent”, then a probability can’t really be used to prove someone guilty because there’s still a probability that the person is innocent even if it’s a low probability. I mean if its an insanely low probability, like 1 in a trillion, then yeah they are guilty, but 1 in a million does not mean impossible.

[@ntdscherer]

The standard cannot be absolute certainty. We might as well just throw away the whole criminal justice system if we were to do that, because that standard is essentially impossible to achieve. And people generally would not be able to really understand the difference between one in a million and one in a trillion, let alone actually be able to meaningfully assign such a probability to someone's guilt, so there's no use trying to pin down an exact number as a standard of proof either.

[@mattschumacher4581]

Nate Scherer I understand that but sometimes we use the term highly likely to describe a 9 in 10 chance or something. We just need to know the difference between a high probability and an very high probability. And then we have to use context and other evidence to determine guilt. Sometimes juries and prosecutors are too willing to send someone to jail.

[@ntdscherer]

@@mattschumacher4581 You're definitely right about that. There are lots of people in prison for crimes they didn't commit, which should be sufficient reason to abolish the death penalty. We also need to get rid of all the junk science police and the FBI use to convict people.

[@mattschumacher4581]

Nate Scherer that is so true. We also need to take some of the money we spend on prosecution and give to public defenders. A lot of prosecutors only care about winning cases bc they are paid better if they prosecute more people but they should care more about upholding the law and prosecuting the right person. Basically we just need to accept the fact that is easy to get away with crimes. But it’s much easier to get away with crimes if an innocent person has already been prosecuted for the crime you committed.

[@ntdscherer]

@@mattschumacher4581 Yes! Totally agree.

[@RUBBER_BULLET]

It took an amateur mathematician in the UK, who happened to read about the case several years later, realise the miscalculation and get in touch with Lucia de Berk in the Netherlands to tell her.

[@henrylorenz8911]

Do you know how small the chance is, that a planet has life on it? I guess we don't exist

[@chandy3859]

When people forget how many the sample are.

[@ZakisHereNow]

But, what are the odds that a person close to the victim would have that exact DNA match? You’re not comparing everyone in the world, you’re comparing people in a local group.

[@ZakisHereNow]

Rick Lokers Are you sure? Pleas explain. My logic: I punch the 10000th person I see. Factoring in everyone in the world. Now factor in my traveling limitations and financials. Does a person in China have the same odds of being punched as say someone in my local neighborhood? So yea taking the worlds population and just numbers, everyone in the world has a 1/10000 chance to be punched.

[@user-lk2vo8fo2q]

it would affect the likelyhood of a match somewhat, but in both directions. if you're only considering some local group (e.g. people in the same state as the victim), then the chance of finding a match is lower because there are fewer people to match with (and so if a match is found, the chance of it being a "false match" is lower). on the other hand, the genetic diversity of a group of people in the same country is presumably less than the genetic diversity of the entire world, so the chance of finding a match within that group would be a bit higher. so you'd in theory get a different number than if you'd just looked at the entire world population, but that isn't exactly what they were doing anyway. also the fact that an experimental sample found 90 when the expected value was 98 would seem to indicate that the second consideration doesn't matter that much.

[@nk361]

18:58 I think you actually did exactly what you were talking against in the video because even if it's one in one million people on earth, like you said, you can easily reduce the group of people who match the DNA by location, gender, age, appearance, criminal record, etc. Which you sort of mentioned, but still mostly made it sound like it could have been any match on earth. You essentially combine unlikely matches to get a larger and larger probability of it being only them. Pretty much all else sounded correct to me though. :)

[@JellyWaltzov]

Ok, this is the most comprehensive and balanced video I have seen on the subject so far. I salute you.

[@Ultrasonix3]

Someone phoenix wright me with an objection

[@rc5989]

Very interesting and informative video. Enjoyed!

[@Aziqfajar]

2:24 I smell friction

[@csipawpaw7921]

One in a million is not that much if you consider the number of people in the world. But then all the people in the world are not all in one city are they? You also need to consider the odds of two people with matching information being in the same place at the same time!

[@complainer406]

Wouldn't the odds be different for a person matching any 5 of the loci from a given sample vs matching a select 5 (i.e. the only 5 that they had)?

[@Tom-vx7qh]

That's like if two dudes were hanging out and one gets struck by lightning and dies, and the other guy is convicted of murder because it's incredibly unlikely for a person to be struck by lightning.

[@Morningstar_37]

Or you go to some person who won the lottery and say "The odds of you winning is so low, you must have cheated!" and then sue them

[@JoseJimeniz]

"What are the odds he's innocent?" I would not, in good conscience, send someone to prison based on odds. I want actual evidence that *he* did it.

[@seventeenpipingounces]

Then it sounds like you didn't watch the entire video and understand the point of it.

[@JoseJimeniz]

@@seventeenpipingounces I did watch it. Which part do you think addresses our concerns.

[@JoostMehrtens]

@@JoseJimeniz So what do you count as evidence, finger prints? DNA? Eye witnesses? They all have a probability of failure.

[@mariareed5238]

in the early 70s when I was young there was a big thing about SIDS - In my town we lost a few babies to it and I can tell you the town would have had less than 3000 people in it - its an awful thing to happen and its horrible that a mother loses not one but two children to it and then gets thrown into jail -

[@spiderwings1421]

Even IF we assume independent events on the SIDS case, looking at the population of the world, this is likely to happen to at least 100 individuals in the world, or around for in the US Edit- lol he literally said the exact same thing 5 seconds after I commented this

[@dragade101]

Dang. I have messy and fairly inconsistent signatures. Like sure counting how close down strokes might show a strong divergent behaviour between two signatures that should be from the same time but that is wild that a court thinks that anyone’s signature is so consistent

[@carterlove]

If your one in a million thee are 8000 people just like you

[@laststand6420]

People are superficially the same... And fundamentally, ridiculously different.

[@disrael2101]

Super facisnating and easy to understand explanation! Please keep posting more similar stuff

[@flobbie87]

"All other wills are invalid.", doesn't make any sense.

[@strebicux6174]

Yeah wtf? Why would she ever write a second will then?

[@DDUU11]

@@strebicux6174 Maybe she had supposed she could start losing her mental faculties later, for whatever reason, and make a worse choice (or write a second will because she forgot the first ever existed)

[@strebicux6174]

@@DDUU11 yeah the mental health one is a good answer

[@calvinmcneil9824]

It would make sense just in case someone forged a new will later on

[@zuhail339]

Please keep making these AMAZING videos Zach ♥️

[@thomashanson3476]

Who’s here after dream got called out?

[@irreleverent]

The calculation for the SIDS mother made me twitch a bit. The data was just so blatantly misused along multiple axes that it hurt.

[@LanK111er]

Just kind of a weird question but are the locations of the horizontal DNA pairs actually independent? I'm gonna do some research but I'd love to know if anyone else knows.

[@thelastviking2039]

My mother signs her name this consistent. I don’t even look when I scribble the letters

[@WiggaMachiavelli]

1:26 "guaranteed" No, we're not. You need 367 people in a room to guarantee that at least two share a birthday. Nothing short of that will give you a guarantee.

[@Topples7]

"Basically"

[@andysmo]

Having 367 people doesn't guarantee it, since some may have the same birthday.

[@benjiboy1337]

Not only is it okay to question numbers, it must be encouraged. That's the process of scientific peer review - question everything, and evaluate the answers that you are given. A strong use of statistics will stand up to scrutiny, and a weak usage will be easy to poke holes in if you press hard enough. This is how we consistently get closer to real truth in a world of uncertainty.

[@huvudpersson7344]

The solution isn't not using statistics in court, the solution is not having a jury of random people deciding the fate of legal cases.

[@jeromeorji1057]

Sure but that would be undemocratic. One hand, you ensure that the jury is "fair" by choosing jurors randomly but on the other hand, the majority of the populace is highly prone to illogical thinking and other fallacious reasoning. Going the undemocratic route consolidates the power to decide the fate of everyone else in the hands of a few, and the few is more easily corrupted than the many.

[@huvudpersson7344]

@@jeromeorji1057 I understand what you mean, but I am not saying that having just one judge is the answer. For example, in the UK they have their system with a jury of magistrates, or like in Sweden (and I'm sure many other countries) Where you have three judges that have a long legal education and a good understanding of the law. Yes, there are some cases where judges can be bought and influenced by others, but a jury can easily be tricked into thinking something based on emotion or things that are completely illogical, and you can be sure that lawyers are aware of this and will use this as much as they can.

[@huvudpersson7344]

And about undemocratic: isn't the most democratic thing having competent people that understand and will use the laws that govern the democracy correctly?

[@HotCrossJuns]

@@huvudpersson7344 The whole point of democracy is that everyone's voice is equal to each other. Now, obviously, there are flaws in this system, but as Churchill said: "Many forms of Government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed it has been said that democracy is the worst form of Government except for all those other forms that have been tried" Therefore, a jury of judges would be anti-democratic as the judges would be considered elites of society that completely controlled the criminal justice system

[@9308323]

@@jeromeorji1057 Truth never cared for democracy.

[@donyt4926]

1:27 Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray Januray

[@42f87d89]

It makes so much sense to use the birthday paradox to explain why you can't just multiply the total number of option by the probability you want! How could I never had thought of that. It's like an extension of the pigeonhole principle.

[@nowonmetube]

He used the birthday paradox wrongly though. He used a probability of 50% _sharing a birthday._ Why 50% though? What are the odds that there's a 100% change they shared their birthday?

[@SgtSupaman]

@@nowonmetube , he used 50% because that is what is commonly used when this "paradox" is presented (because 50% is half and it is really easy to figure out half of 366, which leads people to the initial wrong answer of 183). This figure of 23 is also used because it is the closest one will get to having an equal chance of finding a shared birthday vs not finding one (it is actually about a 50.63% chance that two people in a group of 23 will share a birthday). The reason no one uses 100% in that problem, is because the answer is intuitive and pretty obvious. You would have to have 367 people to have a 100% chance that someone in the group will share a birthday with someone else in the group. Even a group of 366 people will still have an extremely small chance of everyone having a different birthday. And when I say "extremely small", I mean -small enough that I couldn't find a calculator that could figure it out- it is .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000536% (that's 5.36x10^-156 % or a chance smaller than 1 out of an octodecillian googol). However, there are some other interesting points one could use. To get around 90% chance of someone sharing a birthday, you need a group of 41 people (90.25%), to get around 99%, you need a group of 57 people (99.00%), and to get about 99.99%, you need 80 people.

[@nowonmetube]

@@SgtSupaman but still 100% it would NEED to be 366, right? Because even though pretty low, but the chance is there, that everyone of 365 has a different birthday, right?

[@SgtSupaman]

@@nowonmetube , correct. I used 367 as the required group to reach 100% because there are really 366 birthdays (some people are born on February 29th).

[@kronusexodues7283]

"it's not a paradox, it's just a counterintuitive problem" but... that's what a paradox is

[@morisakomasaru8020]

It probably does.

[@chronicallymeee]

I used to do this thing as a kid where I'd essentially try to figure out how likely I am. Like I was born in Canada in 1996. There were 366,200 births in Canada in that year. and approximately 133 million births in the world that year. Giving me a 0.2% chance of being born in Canada. And I used to do this with all sorts of statistics about myself. And given that like humans are unique the likelihood of me being me is less than one in 107 billion. But obviously I exist. I don't suddenly stop being Canadian because there's so little chance of a random kid born in 1996 being Canadian. There's also a 0% chance someone else is exactly the same as me. I was born at home, so I know for a fact no one else was born where I was born when I was. That's before anything else like what my traits are or the rest of my life comes into play. But I think doing this as a kid, really affected my understanding of statistics. From a young age, the "one in a million" turn of phrase really bothered me. I know there are 7 billion people now but at the time it was 5.5 billion range, and I would say if it's one in a million there are 5 and a half thousand people who fit it. Again 366,200 people were born in Canada in 1996, yet it's 0.2% chance a child born in 1996 is Canadian.

[@vainbow4632]

The a posteriori probability of an event having occurred, knowing that it has already occurred, is 1. It seems counterintuitive because that is just not how probability theory works.

[@knights_limit]

I had a hypothesis testing question that I wanted to discuss: imagine you have a bag full of one million pennies, all are fair except one where the probability of heads is 1. You pull a coin out at random and flip it 19 times, getting heads on each. What do you conclude?

[@Topples7]

We want the probability that the coin is rigged, given that we got 19 heads. Bayes Theorem: P(rigged | 19 heads)=P(19 heads | rigged)*P(rigged)/P(19 heads) Expanding out P(19 heads) by cases: P(19 Heads)=(P(19 heads | fair)*P(fair)+P(19 heads | rigged)*P(rigged)) Combining: P(rigged | 19 heads)=P(19 heads | rigged)*P(rigged)/(P(19 heads | fair)*P(fair)+P(19 heads | rigged)*P(rigged)) Plugging in: P(rigged | 19 heads)=1*(1/1000000)/((1/2^19)*(999999/1000000)+(1)*(1/1000000)) Simplifying: P(rigged | 19 heads)=0.34395622 So there's a 34.4% chance the coin is rigged. Hopefully I did that correctly.

[@robertgomez5378]

Using a t test gives strongly significant results to say that the coin is not a fair coin. (a = .05, p

[@knights_limit]

Robert Gomez what if the coin only had 10 flips? What’s the most number of heads we could accept and claim it’s the fair coin?

[@robertgomez5378]

@@knights_limit hypothesis testing is inherently "flawed". The one I've used compares the given data sample to the data that should be expected and draws a conclusion on whether we can reject a hypothesis or not. T tests are used a lot in biology experiments because with bigger data samples and well established population means the results let you say something along the lines of "we are 95% sure this is true for this value range". But typing this out made me realize the test I used is most likely inadequate because after like 5 flips it'll say it's statistically significant but at that many flips we know it could still be coincidence

[@jessejordache1869]

Oh, I heard of this case. I got so angry, immediately, like "you need to have the gavel taken away from you until you put some Bayes in your life."

[@DJTejasMusic28]

This is really good stuff. I wanna become a lawyer and I study advanced stats and calc in school. For me personally, I would love to see more content like this.

[@ceterisparibus42]

I love your videos about probability and statistics! Really good job

[@theproofessayist8441]

It's quite interesting because although I love math - I think utlitarianism or other quantitative frameworks of ethics to be very cringey in my opinion. Regardless this is a very innovative video. Kudos!

[@obviouslymatt6452]

What’s cringey about utilitarianism? And it doesn’t even have to be about quantifying it, it’s just about doing whichever you believe to cause the least harm and most pleasure, rather than judging it by some inherent moral standard or belief, such as “lying is always bad”

[@rudelwolf1591]

@@obviouslymatt6452 well, because you have to quantify to use utilitarianism. Without quantification, the simple question of what decision has the best outcome get's basically impossible. And quantifying in that way is also basically impossible, as the moment you try to quantify the worth of life, happiness, pleasure, pain etc. you will have basically a different perspective for every human in the world. I don't want to say that utilitarianism doesn't have its uses, but you always have to keep in mind that it is not as easy and clear cut as it is often percieved to be.

[@frankhooper7871]

At 4:45 surely it wouldn't matter if the niece had an _earlier_ version of the will, forgery or not, as subsequent will render previous ones invalid.

[@ishworshrestha3559]

Hi I really love your videos. I am right now studying electrical engineering from developing country(poor) Can you make video on how can I do well in future (like getting jobs in USA)

[@abcdxx1059]

Define Poor you moron

[@suyashgarg4005]

Quite an interesting operationalization of "doing well in future."

[@ishworshrestha3559]

@@abcdxx1059 I mean Nepal. I feel like I am wasting my time studying here.

[@watfunstu9086]

with so many people, it is possible for these things to just happen by chance, and it is also important to recognise (i think) that these people that it happens to by chance are more likely to appear in court in the first place

[@wgfuzgvy6016]

Imagine being recommended this video because of the whole dream incident

[@julymorris6367]

This reminds me of when shartpissbaby69 and penisnotfound went through the urmomfat exile arc 😔