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Geometric Distributions and The Birthday Paradox: Crash Course Statistics #16

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Geometric probabilities, and probabilities in general, allow us to guess how long we'll have to wait for something to happen. Today, we'll discuss how they can be used to figure out how many Bertie Bott's Every Flavour Beans you could eat before getting the dreaded vomit flavored bean, and how they can help us make decisions when there is a little uncertainty - like getting a Pikachu in a pack of Pokémon Cards! We'll finish off this unit on probability by taking a closer look at the Birthday Paradox (or birthday problem) which asks the question: how many people do you think need to be in a room for there to likely be a shared birthday? (It's likely much fewer than you would expect!)
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Опубликовано:

8 авг 2024

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Комментарии : 109

@sergior.m.5694 5 лет назад

I feel like I should be paying this page rather than my University

@ThorOdinson2 6 лет назад

"Alas, earwax." -Professor Albus Percival Wulfric Brian Dumbledore, O.M. (First Class), Grand Sorc., X.J. (sorc), S. of Mag. Q., June 7, 1992

@saivishnutulugu5014 5 лет назад

Helpful Hint: If you want to verify if a situation is geometric there are 4 conditions: 1.) each observation can be classified as a success or failure 2.) n observations are independent 3.) p(success) is the same for each observation 4.) Variable of interest in the # of trials UNTIL success

@ncooty 6 лет назад

These examples all rely on independent probabilities. The jelly bean example would require either (a) infinitely many jelly beans or (b) replacement. Otherwise, the probabilities aren't independent.

@EdwardDowner 6 лет назад

Considering each pack is a small sample of a very large population of jelly beans I think it's a valid approximation. You could get an entire pack of cinnamon beans. Low probability, but that's what this is all about.

@ncooty 6 лет назад

+Edward Downer Yeah, I considered after posting that they might be talking about known population probabilities and that the sample characteristics are unobservable to the eaters. (I think she said that there's nothing to indicate flavor before eating, so they wouldn't need to be drawn from an opaque container.) Still, those are the sorts of details I'd stipulate.

@devjyotidey7165 6 лет назад

Yes exactly

@angelcarrillo980 5 лет назад

4:47 Can some explain to me how the 89.3/100 chance occurs before the 10th shot and not after the 10th shot? Can someone explain to me why there is a total of 92/100 chance of making the shot after the 10th try?

@yolandaameny2506 6 лет назад

You’ve saved my A Level Statistics grade! Thanks for making this!

@psyched1639 6 лет назад

The birthday paradox is a very unusual one. Typically, biases make the world seem simpler and more predictable. The planning fallacy, the gamblers fallacy, and base rate neglect paint a picture of a simple world, but the birthday paradox is one of the rare examples of people consistently overestimating the complexity of something. Of course it relies on an oversimplification of the probability calculation, but still, it's odd.

@fendularatsq2317 6 лет назад

so the word paradox is just used for human bias, it has nothing to do with math and statistics that go with it, dumb thing to call it "the birthday paradox", its misleading.

@psyched1639 6 лет назад

Fendula Ratsq I agree that it's a bit misleading in this case. Paradoxes happen when you can prove two different contradictory answers, but in the birthday paradox, you get the mathematical answer and the other answer just comes from our intuition. Birthday paradox sounds better than Counterintuitive Birthday Related Probability Problem, but calling it CBRPP would be more accurate. I'm fine with just calling it a paradox

@unknownpawner1994 6 лет назад

Thanks now i can calculate the rare item drop rates in MMOs

@henrebooysen2513 6 лет назад

Crash course saves my life once again.

@rwhe423723 6 лет назад

For the jelly beans example, the probabilities are assuming some sort of auto refilling bag, right? Because if you ate a non-vomit jelly bean from a regular supply (e.g. the glass bowl), then wouldn't the probability of the next jelly bean also not being vomit decrease since there are less good flavors remaining? This wouldn't be the same kind of example as "pulling black socks from a drawer" with replacement.

@JimFortune 6 лет назад

Ryan Wheeler Like if you only had 20 beans and one was vomit.....

@rwhe423723 6 лет назад

Jim Fortune exactly, then it'd be 18/19 for non vomit on the second pull, or 1/19 for vomit, so they'd stray away from 95% and 5% respectively.

@tomsakmens5571 6 лет назад

I think it just assumes there are a lot of jelly beans. So many in fact, that the probability doesn't change significantly

@JimFortune 6 лет назад

Toms Akmens That would be a really bad simplification if you were calculating odds for playing Russian Roulette.

@tomsakmens5571 6 лет назад

Jim Fortune except this isn't a Russian roulette. Instead of 6 bullets, it is entirely plausible to think that there are plenty of beans

@hcesarcastro 6 лет назад

Statistics can help one determine how much should be waited for such an event to happen. Especially through the study of queuing theory. Will CrashCourse present a video on Poisson Processes and other stochastic stuff?

@jmnunezd1231 6 лет назад

Im totally in love of you ;-)! Outstanding video!

@nivolord 6 лет назад

By the way, cumulative probability of geometric distributions is 1-(1-p)^2, or 2p-p^2.

@francoislacombe9071 6 лет назад

Where did the little bamboo plant go? 8-(

@Dunkle0steus 6 лет назад

with the jellybean example, the chance of getting a vomit flavoured bean increases each time you eat a bean that isn't vomit flavoured, because the number of vomit flavoured beans remains constant while the total number of beans decreases.

@urjaman0 6 лет назад

That's true if every bag is filled with some vomit flavoured beans, but not if the supply is truly random (=you dont know if the bag has any).

@Dunkle0steus 6 лет назад

I disagree. It's true that a random selection of beans may not have any vomit flavoured ones, but what I said is still true. Let's say that you randomly put 100 beans in a bag. Each bean had a 5% chance of being a vomit bean. The number of vomit beans in the bag is some unknown quantity x, but it's likely somewhere around 5 (though they could all be vomit flavoured beans or none of them could be vomit flavoured beans). The quantity x does not change over time, and you would describe x relative to the 0.05 chance of a vomit bean and the 100 beans selected. If you picked 50 beans out of the bag and none of them were vomit beans, you would STILL expect there to be x vomit beans in the bag, which you would expect to represent about 10% of the bag. Because x does not change as you remove other types of bean, the probability of a vomit bean must increase as you pick beans. Situations in which the probability would not change include the later example of making free throws. When picking beans from a finite supply (which we are, according to the example with the box of beans), each successive bean is not independent of the previous bean.

@EdwardDowner 6 лет назад

It isn't true, because that bag is a random sample of a VERY large population of beans. The chance of not having a vomit flavored bean in a 100 bean bag is exactly the same as pulling 100 non-vomit flavored beans from the entire population. In fact that's exactly how the bag was filled.

@Dunkle0steus 6 лет назад

That's entirely beside the point. I'm not saying those two events are equally likely, only that both are possible. I was just stating the extreme examples on both ends, and trying to convey that I understand that a 5% chance doesn't necessarily mean there will be 5 vomit beans in a 100 bean bag. But if you had 1000 such bags, you'd expect 5 to be a relatively frequent number of vomit beans. It's a probability distribution. But my actual point still stands: because the "bag", or in the case of the example used in the video, box has a finite and predetermined array of beans, every non-vomit bean you pull from the box DOES increase the chance that the next bean will be a vomit bean. Because we are working with probabilities, we must consider every possibility weighted against the probability (meaning that the case where 99/100 beans are vomit and you just *happened* to pull the one vomit bean the first time is incredibly unlikely, so the 100% chance of a vomit bean that is present in that case will be vastly outweighed by the much more likely case where there were roughly 5 vomit beans originally)

@tonyleukering8832 5 лет назад

@@Dunkle0steus The free-throw probability probably does not represent a truly random sampling event, because psyche is not considered. From personal experience, I can say that the chance of a successful free-throw attempt may actually decline with continued failure.

@futureDK1 5 лет назад

The orange shirt makes your eyes pop!

@mainaccount4948 6 лет назад

Nice, very interesting

@ShiningDialga 6 лет назад

They actually used the Crimson Invasion pikachu, that's attention to detail!

@vegangelo_29 5 лет назад

1:03 I can hear the jittery breathing. Hahahahahaha

@souravsharma3641 6 лет назад

Can you please do a CC on Film Production Budgeting or How to make a Film Budget according to the script @CrashCourse

@joselucastaneda 6 лет назад

Ready for my ASQ CQE exam

@Danilego 5 лет назад

6:40 pretty scary Big Brother easter egg on the Blu-ray shelf

@citiesskyscrapers4561 6 лет назад

Nice video)

@sleepinonmezzz5374 6 лет назад

Where were these stats videos 2 weeks ago when I had to take a Stats final and hadn’t been to class in since the last exam

@funkysagancat3295 6 лет назад

I love the grass ones!!!!!!!! And the soup ones

@funkysagancat3295 6 лет назад

And the ones our society considers "normal" flavors, of course, I'm no weirdo

@SubscriberswithNOVIDEOS-rm3tn 6 лет назад

Don't worry, I love the grass ones too.

@emeraldemperor2601 4 года назад

7:57 but what if 1 and 2 have the same birthday, then 3 has a 364/365 not 363/365

@henripearson1622 6 лет назад

When the AP Stats exam is tomorrow and you realize CC Stats is not going to cover everything in time :(.

@seanb4063 6 лет назад

same

@eagledudetelevision 6 лет назад

Facts

@ascellaborealis9051 6 лет назад

Henri Pearson Good luck on your exam

@lillyyoung2570 6 лет назад

Henri Pearson *cries*

@MathsHistoryHelp 6 лет назад

Henri Pearson check jbstatistics

@NAMANSRIVASTAVA-zw8tc 2 месяца назад

I loved the pokemon cards example.Because i am a pokemon fan😉

@64standardtrickyness 6 лет назад

Here's an easy way to think about it 20 people leads to 20C2=(20)(19)/2=190 pairs of people who ask each other whether or not they have the same birthday intuitively the even of any pair having the same birthday is negatively correlated so we can think of them "rolling the dice" 190 times thats why this works

@anony_mous2042 6 лет назад

Im taking AP Research at my high school next year, and my teacher wants us to pick our topics now. I want to do something in the field of statistics. Anyone got any suggestions? Thanksss!!

@aurisharicaforte9587 6 лет назад

Please do normal distribution next!!

@marksusskind1260 6 лет назад

I imagined barflies, puke-flavored candies. They're sickeningly sweet!

@Fatima-gq1oo 6 лет назад

Have the AP Stats Exam tomorrow; this video was super helpful!

@lillyyoung2570 6 лет назад

who’s also cramming for AP stats?

@ps374249 6 лет назад

@saivishnutulugu5014 5 лет назад

Me as well

@lucasm4299 6 лет назад

AP Stats group, over here!!! 😂

@alfuccine1484 6 лет назад

Hey, it's me again I found another idea you can make a video since I have a test tomorrow on absolutism and constitutionalism, you don't seem to have any crash course videos I can find on absolutism. Again, I would've loved to watched one of your videos for absolutism for my test.

@bryanwebster7027 6 лет назад

I did the free throw math at the end of every basketball practice. That's why my coach kicked me off the team.

@williamkibler592 5 лет назад

Binom (n,k) = nCk (p)^k * (1-p)^(n-k) geom (k;p) = (1-p)^(k-1) * p -- probablility of a success untill a certain trial, need to add all previous trials to get cumulative probability

@shinxy8389 6 лет назад

Wouldn't the pikachu card example actually be better modeled using the binomial distribution? Since you would purchase a certain number of cards or packs instead of drawing from a pile until you get the desired card

@tashigurung1255 5 лет назад

I agree

@kentkacs3140 6 лет назад

Part 17? Was there a 16?

@rparl 6 лет назад

Ken Tkacs I just noticed that too. The thumbnail had 16, but the title was 17.

@motahidahmed2114 5 лет назад

I agree with both of you

@meanmikebojak1087 4 года назад

What were odds of that?

@seanm7445 6 лет назад

Lol, “stuffed otter"

@Tfin 6 лет назад

0% chance of stuffed otter.

6 лет назад

So where was the paradox again?

@weedking1984 6 лет назад

But I want the ear wax in vomit one theirs is the best ones to get

@sneakrrr 6 лет назад

Now you need to eat 1 bean until you get the vomit bean

@HeidiBialik 5 лет назад

At 6:27 she says 0.04% ("point oh four percent") but 0.4% comes up on the screen.

@Makelka 6 лет назад

With the example of the Pokemon cards and the cumulative geometric distribution, I would suggest instead using the binomial distribution covered in the last episode. Considering that the trials don't end, assuming you already bought 40 cards, when the Pikachu is drawn, the cumulative geometric would not represent the question: "What is the probability of getting one Pikachu in these 40 cards I've bought?" which I would think is the question you would want answered in this case. The cumulative geometric would, with larger amounts of trials, severely overestimate the probability, 18 vs 16 % with 40 cards, 39 vs 30 % with 100 cards.

@Makelka 6 лет назад

Note that the question: "What is the probability of getting at least 1 Pikachu within these 40 cards?" is answered by the cumulative binomial distribution and evaluates to the same probability as the cumulative geometric.

@rkpetry 5 лет назад

*_...we are left with the concern that probability theory isn't looking at the whole picture-like deciding where to take this year's vacation is a small bump in the budget, but a large bump might leave you without a job when you return six months later, or, what if your arch rival wins the lottery, or maybe worse what if your spouse wins the lottery and decides to move the family to 'X Isle' and retire til you divorce for boredom and spouse can marry somebody else, (If families were voting units we wouldn't have voting per person)... Statistics as good-vs-bad, lacks the substance of being, worthy..._*

@haeleon654 6 лет назад

The red ones are the best because they're either Cinnamon or Cherry.

@NaihanchinKempo 6 лет назад

Here is some ez poker math. The rule of 4 and 2. . IF you have a Draw 4 to a straight and 4 to a flush. The math is 4 X outs, and 2Xouts. Outs, being cards needed to hit the straight or flush, so. IF you get a flush draw the the flop in Texas Holdem. you have 9 cards to hit so it's 9 X 4 + 1 OR 2on the turn. AND 9X2+2 on the river. SO on turn you have a 33% chance to hit the flush, and a 20% chance to hit on the river. Pot odds you divide your call, into the pot. IF they are the same. 33% and 20% of the pot OR cheaper. it's a good call. Otherwise, in the long run, the Pot costs you more then the % chance to hit a flush\straight you should fold. open ended staight draw has 8 cards 4 on each end and flush draws are 9 cards. that said, because the dealer kills a card each street and many player share cards you need lowering your % buy 2- 3% is a good idea.

@SeventhAlkali 6 лет назад

What's the probability I pass my AP Statistics exam?

@oscarmoreno2585 4 года назад

@johnnyvaughan5841 6 лет назад

Alas, earwax!

@MYSTERY_STORYSHOWER 5 лет назад

Where’s the Guy in beginning of the Video?

@dulceele2967 6 лет назад

Its 17-5 and its my birthday

@vasishtvemuri4181 4 года назад

"Probability assigns numbers to common sense", my common sense tells me that, the probability that a statistician can be such a good writer is pretty low!

@qinyuping2823 4 года назад

Geometric Distributions and Binomial Distrubutions sound the same to me

@tjdriver7098 6 лет назад

I smell like BEEEEEEEEEFFFFFF I smell like BEEEEEEEEEFFFFFFFFFFFF

@wenhong5852 5 лет назад

Darn it now I want to buy Pokémon cards

@jonathanjernigan3865 6 лет назад

Bad basketball players and Shaq.

@briieme 5 лет назад

The guy at Target is 1000% my ex- wow

@RilianSharp 6 лет назад

my cousin was born on leap day.

@jarek5220 6 лет назад

This probably should be #16 not #17, what's more it's not appearing on Statistics playlist

@lerolerolerolerolero256 6 лет назад

The vomit flavoured jelly beans joke is taken from "Harry Potter and the Philosophers stone".

@tjdriver7098 6 лет назад

THIRD

@kachnickau 6 лет назад

I was expecting, that she will continue bravely trying another beans during the video.. you know.. just for science ♥

@tpprice3 6 лет назад

As someone who specialized in stats in college this was the most confusing lesson I've seen on here. I guess i now know why folks don't know statistics

@SubscriberswithNOVIDEOS-rm3tn 6 лет назад

Like if you caught the harry potter reference (the non obvious one, not the bernie botts jelly beans).

@C05597641 6 лет назад

testy

@SubscriberswithNOVIDEOS-rm3tn 6 лет назад

Let's find out how long it will take for this comment to find two people with the same birthday. I'll be person #1 with February 2nd.

@HarrisChoudhry 4 года назад

Cringe

@JCResDoc94 6 лет назад

it cant go to infinity at all. metaphor has no place in math. it is items like this (& poorly defined multiple infinities) that make ppl feel they cant understand math topics. try it again w/ actually having infinite beans & samples. or choose clarity.