Q; Which is an example of a hypergeometric distribution?

Question

1.Which is an example of a hypergeometric

distribution? Please explain.

a) probability of the number of aces in a

seven-card hand

b) probability of each sum when two dice

are rolled

c) probability of a number being randomly

chosen from the numbers 1 to 10

d) probability of the number of times a 3

occurs when rolling a die six times

Answer 1

The correct answer here is (a), lets discuss why...

The Hypergeometric distribution is a special discrete probability distribution, all the possible answers here are discrete so we have that covered.

The Hypergeometric distribution itself describes the probability of selecting k successes in n draws without replacement from a finite population N that contains K successes within the population.

So to summarize the features of this distribution:

N = size of the finite population

K = number of successes in the population

n = number of draws from the population (think of this as a sample of the population)

k = number of successes in our draws/sample

So, how does this relates to answer (a)...

Here we have a population of 52 , all the cards in the deck, so N=52. Of the 52 cards we are going to consider having an ace a "success", so K = 4 as there only exists 4 aces in the deck. We draw a 7-card hand so n = 7, this is our sample. Lastly the number of possible aces in our 7-card hand is k.

Therefor we say that k is a random variable with the possible values of 0,1,2,3, or 4 and follows a Hypergeometric distribution.