The Illusion of Certainty: Risk, Probability, and Chance

Stuff happens. The weather forecast says it’s sunny, but you just got drenched. You got a flu shot-but you’re sick in bed with the flu. Your best friend from Boston met your other best friend from San Francisco. Coincidentally. What are the odds? Risk, probability, chance, coincidence-they play a significant role in the way we make decisions about health, education, relationships, and money. But where does this data come from and what does it really mean? How does the brain find patterns and where can these patterns take us? When should we ditch the data and go with our gut? Join us in a captivating discussion that will demystify the chancy side of life.
This program is part of the Big Ideas Series, made possible with support from the John Templeton Foundation.
The World Science Festival gathers great minds in science and the arts to produce live and digital content that allows a broad general audience to engage with scientific discoveries. Our mission is to cultivate a general public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future.
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Visit our Website: www.worldsciencefestival.com/
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Original Program Date: June 2, 2011
MODERATOR: Marcus du Sautoy
PARTICIPANTS: Amir Aczel, Gerd Gigerenzer, Leonard Mlodinow, Josh Tenenbaum
Josh Tenenbaum and an experiment in ESP. 00:00
Risk, Probability, and Chance. 02:54
Marcus du Sautoy's Introduction. 06:32
Participant Introductions. 07:27
Are we good or bad at interpreting numbers? 09:45
The Monty Hall problem. 16:00
The fight or flight math means we understand numbers? 21:50
The "numbers are important" experiment. 25:33
VerizonMath: Verizon doesn't know Dollars from Cents. 29:30
If you play a lottery and there is 1 winner in a 1000, what is your percent of winning? 35:30
How well are our brains tuned for evidential data. 39:33
What is the birthday problem? 45:15
The way probability's are phrased are as important as the numbers. 53:31
Do we have a conception of a million? 01:03:28
What is a prior? 01:09:05
Josh Tenenbaum ESP experiment results. 01:15:19
"Numbers are important" experiment results. 01:20:45
How do we get a statistical society? 01:25:25

[@WorldScienceFestival]

Hello, KZbinrs. The World Science Festival is looking for enthusiastic translation ambassadors for its KZbin translation project. To get started, all you need is a Google account. Check out The Illusion of Certainty: Risk, Probability, and Chance to see how the process works: kzbin.info_video?ref=share&v=BcMuYhoL38A To create your translation, just type along with the video and save when done. Check out the full list of programs that you can contribute to here: kzbin.info_cs_panel?c=UCShHFwKyhcDo3g7hr4f1R8A&tab=2 The World Science Festival strives to cultivate a general public that's informed and awed by science. Thanks to your contributions, we can continue to share the wonder of scientific discoveries with the world.

[@roncox4048]

Glad to see you remembered to list Marcus on this occasion

[@Pabloskatepk92]

Why are all the speakers male?

[@johnnycharisma162]

@@Pabloskatepk92 Because it’s washing day.

[@JohnLee-vi7us]

5⁶6⁶⁵5th z a

[@deenagleason1225]

Ll cool l

[@WoundedEgo]

A while back I had a Quantum mechanic fix the brakes on my car. I asked him if they were okay now. He said , "Probably, but we won't know for sure until you step on them". :o)

[@chrisbrown8640]

Only 2 certainties in this life death & taxes.................well....maybe.....

[@paulsherman1023]

The analogy is spot on.

[@IB4UUB4ME]

👍 Nice!

[@whizzer2944]

My car is so complicated I need a mechanic with a degree in quantum physics well nearly .

[@AlienRelics]

"Yes and no" makes a funnier punchline. Or not.

[@gvardon]

The discussion of false positives in medical testing and anchoring were key points in this discussion. Policy makers should be aware of statistics in making policy including imposing medical tests.

[@markganus1085]

it's nice how everything seems to be easy to explain away through probability and permutations

[@fiikahlo]

It'd be nice if the host didn't interrupt the people trying to answer his question 😑

[@avajoyporter9064]

I absolutely loved this group of guys. Smart men and very interesting. I actually enjoyed the lecture and laughed during certain parts. It was actually fun. It made me think and question everything. The host was fantastic and interacted with the guest perfectly. You guys are great. Thanks for the information and knowledgeable panel. Also, thank you for the great host who kept my attention and asked the questions and comments that I myself was thinking. Great Lecture and awesome sense of humor. I see that this was originally 3 years ago when it went live but it still is great information and useful information.

[@JurijFedorov]

The moderator is making this discussion worse, not better. He often speaks when they are explaining complicated stuff which makes it harder to follow their arguments. He should really try to remain quiet when they are explaining stuff. At least ask about stuff afterwards. Not during an explanation.

[@Taylor_in_Southern_Oregon]

Could not agree more, in fact you're being too polite to him. He needs to STFU. It's as if he thinks the show is about him.

[@Watchingthesim]

His t-shirt says he ate scientists....thought it was strictly a math vs science thing but its a 80% chance the constant interruptions might be relation

[@matttenderholt4744]

@@Watchingthesim lmfao!!! Still awesome watching and wondering how stupid most of my doctors might be with math.... Hope you and anyone else reading along, finds the most amazing reasons to smile in the year to come......with out a mask as well😉 Peace and love 💕

[@Redflowers9]

I'm glad they all got along in the end.

[@DanielBrownsan]

WHY DID NOBODY FIX THAT FREAKING MICROPHONE, OH MY GOD....

[@joshuaerkman1444]

I read your comment at 37:30 and thought "what microphone" then 38:04 "oh THAT microphone"

[@SuperBhavanishankar]

@@joshuaerkman1444 data is important

[@Chaosaddict1001]

Why did josh and his anxiety mess it up... The noise you hear is his mic brushing against his shoulder. Nothing wrong with the mic. He's just to awkward to realize it

[@MrDamcor]

It is amazing how many words some people can SAY to actually TELL very, very little.

[@MrVaypour]

hahahaha so true.

[@SuperBhavanishankar]

verbose

[@ConversationswiththeAI]

Thank you... a few moments in I had the "esp" feeling that this video was a waste of time so I should checked the comments to find this...

[@CoreyWoosCHANNEL]

It's amazing how many people ignorantly scrutinize things when they KNOW very, very little.

[@purplepeopleperson3815]

Now that's telling! : )

[@patchy5067]

These guys are great. My mind although was pinging back and forth with dark matter and laughter. Measurable with magnitude and absence. Meaning... Lets go fishing...

[@cosicave5179]

This was probably interesting. The problem for me is that the poor sound quality made it very difficult to be certain.

[@virvisquevir3320]

It depend's on Monty's knowledge and motivation. Behind two of the three curtains is a goat and behind one curtain is a car. And we'll assume that Monty knows behind which curtain the car is. 1) if on every episode consistantly, regardless of whether the contestant initially guessed the car curtain or not, Monty opens a curtain with a goat behind it, then the contestant has a 2/3 chance of winning the car if he switched and a 1/3 chance of winning the car if he doesn't because Monty will not open the curtain the contestant chose nor the curtain that has the car behind it. That means that from the two curtains the contestant did not choose, one has been eliminated as the car curtain, thus the remaining curtain doubles the chance of having the car behind it, jumps from 1/3 chance to 2/3 chance of having the car behind it. 2) If Monty wants to save the show money and tries to throw off the contestant from his initial right guess to a wrong guess, and Monty assumes the contestant knows the odds as explained in #1 above and will switch, then Monty will only open a goat curtain if the contestant initially chose right, in which case the contestant has a 100% chance of winning the car if he stays with his initial guess. 3) If Monty and the contestant start playing psychological games and Monty start trying to guess what the contestant knows or suspects and the contestant starts trying to guess if Monty is trying to throw the contestant off, as in example #2 above, then the contestant has a 50/50 chance of winning the car by staying to his first choice curtain after Monty has opened a goat curtain. If the contestant can gain insight into Monty's motivations, he can increase his chances of winning accordingly, fuzzily.

[@ritataylor4646]

My fav subject and therefore a must to watch

[@ridlespriger2120]

Show you right when you know you right ⚖⚖

[@innercreator7194]

Really enjoyed it! Thank you it was informative and entertaining!

[@whizzer2944]

Good for you , I didn't learn a thing , to much waffle .

[@mamunurrashid5652]

Thank you....

[@KevIn-oz5sz]

Lol my guess was h h t h t when he first mentioned it. I paused the video half way through to go to the shop and continued with the video. Then he said the result was H H T H T and I couldn’t believe it I thought I was hearing things I actually got it right. WOW!! Now I wish I had put a comment up before I knew the answer.

[@mariomenezes5974]

Amazing & fun.

[@ursamajor3275]

What is the theorem that was mentioned to draw pareidolia such as the dots in the stars to delineate objects?

[@Pabloskatepk92]

The assumption that needed to be emphasized is that Monty ALWAYS opens where there is a goat, and there is only one car. Therefore, there are 2 cases out of 3 in which the car is not where you chose. If he intentionally doesn't show you the car and you play three times, 2 out of 3 times you win if you switch. That is clarity.

[@bjornragnarsson8692]

No, the assumption needed to be that Monty randomly offers a new door without knowing whether goat or car.

[@erictaylor5462]

8:10 Drunkard's Walk was one of the best books I've read. HIGHLY recommend it!

[@behrad9712]

Great discussion especially in case of safety engineering and risk of people's life, we need 3 discipline to solve this problem: stat(math)+philosophy+physics

[@acemediav]

26:05 finally someone said it

[@SuperBhavanishankar]

lol

[@ReasonableForseeability]

Yes! He said SU but he shoulda said STFU.

[@AOk-by4pi]

In case anyone is wondering, the 3 choice problem Parade article they’re talking about was written by Marilyn vos Savant. Just thought I’d mention it since nobody else on the panel did.

[@fritsvanzanten3573]

19:40 These numbers about risk per mile are well known, but you never decide about miles but about trips. So the risk should be per trip, be it to the mall, be it a holiday destination.

[@koori3085]

What about a trip to the mall during the holidays, while on holiday?

[@abevan71]

The birthday probability is a typical compound ratio: The first set of numbers range between 1 and 31, and then it runs through a further range between 1 in 12. This is why the results are different to other binary results that are only true or false. The more complex and layered the data, the higher the chance is of a match. It's almost like a field detects the ranges and cross calculates to increase the rates of coincidence.

[@wheeler68]

Nah, it works exactly the same if everyone involved is assigned a random number from 1 to 365 or if you split the year into seasons (1-4) then months within that (1-3) then weeks within that (1-5) then days within that (1-7). A purely cosmetic distinction.

[@Redflowers9]

That mathematician was awesome.

[@KarlHainer]

A great debate.

[@orestiskopsacheilis1797]

Hello everyone, Great talk, really enjoyed it. Can somebody please recommend a couple of papers that encapsulate the concept of understanding via diagrams that Josh Tenenbaum brings forth at about 43:00? It doesn't have to be a paper by him but I would appreciate if it came from a cognitive-science background. Thanks!

[@NenevieVillando]

+Orestis Kopsacheilis found anything?

[@orestiskopsacheilis1797]

+Nenevie Villando Nope, for better or for worse, Josh is very prolific with his academic publications so I wasn't able to track a single paper that does the trick...

[@robertw2930]

Heads I win, tails you lose.

[@aaabbb-py5xd]

So long as you lose and someone else wins

[@Moronvideos1940]

I downloaded this .... Thank you

[@SuperBhavanishankar]

after a couple of years again wow

[@chessdominos]

At 13:36 They stated wrongly The Monty Hall problem: 1 There are always 2 goats 2 The host Monty Hall always knows where the car is. 3 Monty Hall always open a door showing a goat

[@TheDavidlloydjones]

Incorrect. There is always one goat.

[@efreimanis]

It is very hard to focus on conversation and point when everyone is just jabbing all together. I guess i was expecting more scientific approach after watching interview with Jim Simons.

[@curtcoller3632]

I wasn't.

[@tmarkhightower3301]

I watched this on 11/26/2020 and to me it helps to show how easy it would be to bamboozle the public on anything related to numbers and probabilities and uncertainties, such as Rona Virus and Elections.

[@NoActuallyGo-KCUF-Yourself]

Seen any evidence of bamboozlement yet?

[@UtraVioletDreams]

Interesting discussion initialy about math, risk and certainty, well I did not realise it untill 1:25:15

[@Abhothra]

Great video, but can someone please explain the joke on the presenters t-shirt ?( I are scientists) Is it a play on plural / single form or something else ?

[@justtrolin]

the weight of the word does indeed have a very real utility in the representation of the data. It's why tutors are a thing in nearly all subjects. no one is questioning the professor's knowledge on the subject, instead, it's the approach or the cosmetic medium that can have a key influence in the mind struggling with the content. additionally, I'm certain that coincidental inferences would reveal that the weight of the word, implicature, and even how it is said will be noted to have an influence on the responses from the audience. there is a need for a metric value of words, determined by the majority of the populous to go any further than this assumption. likely to be made more interesting if it is revealed that personality types weigh words differently.

[@davidwayne1333]

Whew ..... wipes brow sweat !

[@ahreumlee4533]

This was a lot of fun

[@mesplin3]

The German man taught Bayes Rule very simply. That was very good.

[@TheBothWorlds]

Am 1min 28sec in. and I already like this guy.

[@KipIngram]

22:00 - the reason people worry more about flying than driving is simple: you are *not in control* when you're sitting in an airplane passenger seat. You have placed your life into the hands of someone else. Of course, you're not *entirely* in control of the situation when you drive, either, because there are other drivers on the road. But human psychology is what it is, and that sense of having our hand on the wheel and our foot on the brake or accelerator is *comforting*. It takes a rational effort to set that aside and embrace the true situation.

[@Mac2point1]

That phone call recording was painful

[@samidebo]

brilliant but I’d prefer if there were some editorial management from reputable journals also

[@msalmanshalmani193]

Important for practical life

[@iggypopshot]

Damn good.

[@uncljoedoc]

Thanks for this video. I'm asking for feedback. Take Deepwater Horizon Gulf disaster. What is the prior probability of this happening? Does a Bayesian mindset gloss over warning signs in high stakes low probability situations? I must add that I guessed the esp experiment sequence exactly before he completed the coin tosses. That's weird

[@bjornragnarsson8692]

Weird? No. Coincidence? Yes.

[@bwhaz]

This is why I hate trying to do Maths in my head. ...So easy to mess up unless things are kept in place and I can stop worrying that I have things correct in my head.

[@user-kk5gq3ch9s]

nice video

[@DevInvest]

I probably stumbled on this by chance.

[@EmdrGreg]

My guess: Josh didn't actually toss HHTHT. He said that's what he tossed because it was the most likely result the audience would predict. The graphs he showed were what individuals predict independent of what was actually tossed. So if you or anyone did this with an audience, you should say that you tossed HHTHT, or TTHTH [either of these is coded as 00101], and you will get a disproportionate number of people who are awed because they seemed to pick up the 'psychic' cue. Again it's a guess that leading with heads (HHTHT) is more often chosen than leading with tails. He also puts his hand to his head, which might be a kind of light hypnotic signal to lead with heads. This all shows in a fascinating way that people are not so good at behaving randomly. Patterns are pervasive and we seem to be brilliant at picking up on them.

[@jozbornn]

Greg Scott I would be interested in knowing the source for this, because I also selected 11010.

[@julienparise6834]

Greg Scott We call this learning and behavior: the sign he made was a hand over the head. Thats why a good portion of people put HH two times at first, since the sign was not really "clear" and the poor chance that 3 times heads flip in a row, the 3rd flip, people switched to more 50%, starting to understand that this was a "bullshit" message. Maybe this group of people believe they are smarter and understand "the tricks" quickly or some kinda. That a still hypothesis or probability For my part, I choose HHHHH (00000) like a good proportion too, because he just made the same sign over and over and the sign was related to his head (hand over the head).

[@EmdrGreg]

I think you meant to respond to Josh Osborn not me, but I think your view is reasonable.

[@nmarbletoe8210]

Josh Osborn i think when we try to make a 'random' series we always want it to be balanced H vs T, but not too balanced. Thus we don't choose HT or TH to start; too balanced. Thus we choose two H (or two T) to start with, then have to balance that with a T. Then if we next put HHTT that's too balanced, so we do HHTH. but then the ratio is 3:1 which is not balanced, so the last one has to be a T. in short, we take balance to be too important in small series of random numbers. it's so ingrained it's hard to avoid. when i try to make a 'random' series of 6 numbers it often comes out a palindrome. i watched Lenny Susskind do exactly that in a Stanford lecture, lol.

[@EmdrGreg]

No argument from me, Astarii. I understood the basics of the video. Just making the observation that Josh intentionally allowed what he knew the dominant audience reaction would be to be in synch with what he claimed his coin toss was. It's not a flaw of any kind, although it would have been better for him to admit it. He knew what the audience would predict, and he decided ahead of time that his 'coin toss' would be in line with the prediction. I don't for a minute believe that he actually tossed HHTHT. That's what he knew the audience would derive as it's 'random' guess. That's my point, Astarii-- that's all.

[@jessstuart7495]

Probability of Precipitation is the product of the confidence rain will occur times the fraction of area that will experience rain on a given day. It should be equivalent to the probability any given location will experience any measurable amount of precipitation on that day.

[@jamesharris5156]

Let them talk!!

[@maxximusfain1067]

Anyone recommend it?

[@Gootsffrida]

Wow talk about bringing a show to a grinding halt with those slides lol

[@darksoul479]

I knew that flying was safer than driving, I had no idea it was numbers like that. Wow!

[@shahinarya]

Wonderful program...

[@visionshader6549]

So this is where Kevin from Vsauce2 got the idea of his latest video

[@clf6139]

yes but to deduce an answer from numbers is good i suppose, but we use diagrams when communicating the answer so people can understand the answer that is being proposed from the numbers. the use of numbers in deduction apparently gives less error than diagrams to limit the subjectiveness in a visual. but to communicate, diagrams i think are better because the point is to communicate not to infer..is there anything incorrect in my logic here ?

[@clinstar3237]

That Canadian phone call reminds me of how I talk to you guys. 🙃😉🤔🤘🤬

[@fifikusz]

The result of the numbers of people, who new, that one out of onethousands were actually 0,1 percent is frightening....

[@futureproof.health]

A transcript for this would be much appreciated.. the youtube transcript is only a few minutes long from the intro.. ???

[@Moronvideos1940]

i downloaded this

[@Zoharargov]

This is a nice and lively lot. Best pannel evaar!

[@TheDavidlloydjones]

"panel" perhaps?

[@user-hg3nz3ix9r]

Is there proof that holding you hand agains your head helps transmit mental images?

[@karlschwinbarger105]

The various time wasting pursuits to use the audience present to test for probability were huge empty spaces of time for us at home watching this. "Nothing" the second video presented here in this series was much much more interesting.

[@andreasb.769]

Interesting: the German gentleman needs to point out that Berlin is in Germany, instructs us not to behave as "a little child" in front of the doctor, labels certain doctors or journalists as "hopeless cases", ... a discourse based on an unconscious stance perhaps similar to a contemporary current in the politics of his native country towards fellow human beings?

[@dennykeaton9701]

A modern Einstein

[@NoActuallyGo-KCUF-Yourself]

If a million things that each have a one-in-a-million chance of happening could happen every day, then it would be expected that every day a one-in-a-million event will happen.

[@lediableblanc9399]

Yeah, but not to you

[@E_Clip]

This could have been a very interesting program if the guests could actually articulate their thoughts in a more meaningful way. Im not saying they dont know their stuff, but imo they failed to communicate effectively with the guests and us for that matter.

[@sargdavid]

no, that’s just you man :)

[@bobaldo2339]

As a character in one of the Doctor Dolittle books (or was it an Uncle Wiggily book?) said, "Only dopes are positive."

[@SnakeEngine]

So, is the illusion of certainty certain?

[@xSleazyAirplane]

His microphone... lol

[@shizzle5150]

Made it very hard for me to finish.

[@DanielBrownsan]

As an A/V nerd, that almost made me turn it off. Someone needed to swoop in there and get that shit fixed.

[@ihorro]

How strange! There is no date on the stage,so the festival is lost in time for the web-audience.

[@pcamnesty7518]

Ihor Yasinski The date is in the description dummy.

[@MAT3RO1]

48:19 Marvelous! Haha

[@muratadas8974]

Never have I enjoyed a Topic on a Subject I hate so much ( Probability / Statistics / etc,.). Illusion 100%. See the topic summed it up

[@32266ms]

What a great talk and demonstration. Really let's people know that even mathematicians find math challenging and they can have somewhat poor arithmetic skills. It's not bad to be wrong. It is bad to either not own up to it or not learn from it. On the coin flip thing. p(guessing it correct) = 1/32, not < 1/10,000 (1:16:18). 1/32 = (1/2)^5. The sample space has 32 unique events in it each with the probability of 1/32. So the probability of getting the correct sequence by chance is 1/32 and not less than 1/10,000. Unless I've misunderstood some part of what his experiment was or what he said in his discussion - but I think not. Really great stuff! I looked up the verizon CSR call and listened to the entire thing - VICARIOUS AGONY ensued.

[@stabiljka]

What is Verizon CSR?

[@satoruchibana]

Uncertainty is part of life and its what makes this movie we call life interesting. Everything has a purpose and trying to will it is what gets us frustrate and depressed. Become like water is what Alan Watts is trying to say I think. Check it out.

[@TheWolferinDenver]

How do know everything has a purpose?

[@kilikikoparick7560]

Of course they do a question/game in beginning. Just to have you wait to the end to see the answer/probability. This was the only way to get you to watch this joke . My bet there is a ton of subliminal messaging going on in this one warning do not watch hazard to health

[@VideographerExperience]

OK, I was just pondering not several hours ago that the odds are greater of dying in the car on the way to the airport than in a crash in the jet airliner...this keeps happening recently. It's like I'm on the probability tail.

[@professordrabhijitsayamber2299]

Om pure and applied

[@gvardon]

Games of chance and war games and investing are good ways to get a feel for probability and decision making. The best decision in a war game and in investing is one in which the probability of a positive result times the value of a positive result minus the probability of a negative result times the value of a negative result should be greatest. A neutral event can be given zero value i.e neither positive nor negative. The probabilities times value of the occurrence should be summed. But how does one measure probabilities especially of unexpected events and the corresponding values correctly? Also to win in a game the opponents reactions should be correctly considered and his moves adroitly countered. Thus I would argue good decision making is an art as well as a science. And experience helps to make good decisions.

[@mikes9620]

+Gary Vardon prize49(dot)blogspot(dot)ca Lotto649 Research. Good Luck

[@kamleshgya6694]

Marcus de Sutoy should listen, in this things Probability, We can not think we are the most authoritative..

[@bradkalbfleisch5379]

A check at large.

[@AdamRBusby]

the coin toss - halves the correct people 5 times. eg half right each time. 400 sample - 200 after 1 toss, 100 ~2, 50~3, 25~4, 12'ish after 5. Nothing to do with most likely pattern. Each event independent and halves the correct sample - or am I missing the whole point?

[@apburner1]

***** (1/2)^n , where n is the number of coin flips.

[@peterp4753]

This guys just amusing themselves

[@manmeetworld]

Why doesn't the closed caption work?

[@marcef100]

The guy in red talks way too much

[@i4qall]

***** he,s the

[@1CAATMAN]

+Marc Hamilton u talk too much, so shut the fuck up

[@marcef100]

1CAATMAN sorry catman I'll leave your bf alone

[@1CAATMAN]

***** Why thank you. Oh by the way, I am curious if any of your parent's children lived? ilmfao

[@DanielBrownsan]

I was hoping it would be like Star Trek and the guy in the red shirt would get killed.

[@pascalbercker7487]

Very prescient ... @01:25:00 ... they discuss the need for a "risk literate society" - to correctly assess the cost and benefit of various actions ... we might not have been in the fix we are in today with COVID ... who knows ...

[@isaacculents]

daniel kahneman would also have been a very capable person if he was invited! but overall a great panel

[@arkalgudnarayanamurthyshas8976]

very stimulating; but representativness sampling was not discussed; definitions were omitted

[@johnprint5410]

this might be a dumb question but isn't your chance of wining is 50/50 due to the fact that there's only two possible outcome. either you win or you don't.

[@wheeler68]

Let's play a game. I have a sealed box. Inside is one red ball and ninety-nine white balls. If you reach in without looking, and pull out the red ball, you win. If it's white, you lose. Those are the only two options. Win or lose. Is it 50/50?

[@uncljoedoc]

Let's say I am filling a lottery ticket six rows five columns by guessing and filling in the placard. If I group my six numbers in the right upper corner do I have a less chance of winning then if spread the dots evenly around the board. Is there a spatial array probability distinct from temporal numerical probability? The natural frequencies idea appreciated.

[@mesplin3]

I don't think it matters.

[@uncljoedoc]

I was hoping for a thought that there is a spatial distribution probability, in addition to a temporal succession probability.

[@MsSashbar]

The is no difference between filling 1,2,3,4,5 or any other combination of numbers.

[@lediableblanc9399]

Have the winning lottery numbers ever been 1,2,3,4,5,6,7,8,9? In practice as opposed theoretical probability...it matters

[@lediableblanc9399]

How does actual probability pan out? Have there been studies? If there are four items in a hat, in practice does the odds of drawing one end up being 1 in 4?

[@matiasss550]

So why doI need to switch my option? min 15:07

[@acemediav]

11:15 underrated joke lmao

[@NesrocksGamingVideos]

If I could hear it

[@gwasoulja2751]

When you break it all down its just theories and nerds with imaginative minds

[@lizbeveridge]

That's poetry you write.

[@iownedzezima]

The probability that you guessed the correct coin flip sequence is 1/(2^5) or 1/32 which is represented in decimal by 0.03125.

[@TheDavidlloydjones]

That's roughly true and is certainly true of an "ideal" coin. In the real world all coins are biased and almost all coins in the currencies of Western nations are slightly biased toward heads.

[@slappy420usa]

Calculated Risk is quantifying uncertainty. Uncertainty is the progenitor of risk. Pareidolia.

[@canal_vhs]

Please activate subtitles

[@User-uj7nz]

The algorithm was correct today.

[@klz7618]

I think the heads, heads, heads, heads, heads, for the coin flipping at the start was due to the guy placing his hand on his forehead and signaling to the crowd after he did each of the coin flips. people thought he meant heads. Communication failure. lol