Question

From 22 potential women jurors and 25 potential men jurors, a jury of 12 is chosen at random. Let X be the number of women selected. Find the probability mass function of X.

Answer 1

The probability mass function is:

`P(X = x) = h(x,47,12,22) = (C_(22,x)*C_(25,12-x))/(C_(47,12))`

Explanation:

The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability mass of the hypergeometric probability distribution is given by:

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

22 + 25 = 47 jurors, so
`N = 47`

22 are women, which means that
`k = 22`

Jury of 12, which means that
`n = 12`.

Thus

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

`P(X = x) = h(x,47,12,22) = (C_(22,x)*C_(25,12-x))/(C_(47,12))`

Which is the probability mass function.