Cloud anyone show me the equation for Hyper geometric distribution is?

Question

PLease work an example showing a step by step on how you got your answer.

Answer 1

First, let's define the combination function "x choose y", written as

Com[x, y] = x! / (y! * (x-y)!)

where ! indicates the factorial.

The hypergeometric distribution describes this situation:
"We need to find exactly N copies of a object when we select S objects without replacement from a pool that contains C copies of the desired object, and T total objects"

The equation that tells us this probability is

Hypgeomdist[N, S, C, T] = Com[C, N] * Com[(T - C), (S - N)] / Com[T, S]

Example: We want to find the probability of drawing exactly 2 aces when we draw 5 cards from a deck of 52 cards, and 4 of them are aces.

Hypgeomdist[2, 5, 4, 52]
= Com[4, 2] * Com[(52 - 4), (5 - 2)] / Com[52, 5]
= 6 * 17296 / 2598960
= 0.0399298

So, the probability of drawing exactly (not "at least") 2 aces is 3.99%. If we then wanted to know the probability of drawing zero aces in 5 cards, we simply calculate

Hypgeomdist[0, 5, 4, 52] = 0.658842

So, there's a 65.9% chance we'll get no aces when choosing 5 cards out of a deck of 52 that contains 4 aces.