Question

A jury pool consists of 32 people, 16 men and 16 women. Compute the probability that a randomly selected jury of 12 people is all male. Give your answer accurate to at least six decimal places.

Answer 1

The probability of selecting male is $p=\frac{16}{32}=0.5$

number of people selected $n=12$

$q=1-p=0.5$

$P(X=x)=\binom{n}{x}(p)^{x}(q)^{n-x}$

$P(X=12)=\binom{12}{12}(0.5)^{12}(0.5)^{12-12}=1(0.5)^{12}=0.0002$