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

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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[sergior.m.]

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

[ThorOdinson]

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

[saivishnutulugu]

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]

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.

[yolandaameny]

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

[rwhe]

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.

[angelcarrillo]

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?

[nivolord]

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

[psyched]

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.

[unknownpawner]

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

[hcesarcastro]

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?

[henrebooysen]

Crash course saves my life once again.

[Dunklesteus]

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.

[francoislacombe]

Where did the little bamboo plant go? 8-(

[standardtrickyness]

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

[emeraldemperor]

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

[williamkibler]

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

[ShiningDialga]

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

[NAMANSRIVASTAVA-zwtc]

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

[Danilego]

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