Question

14. A jury pool consists of 30 people, 14 men and 16 women. Compute the probability that a randomly selected jury of 12 people is all male.

Answer 1

Total number of people in the jury pool = 30

Number of men = 14

Number of women = 16.

Let the probability of selecting male be p, so that;

$\begin{gathered} p=\frac{14}{30} \\ p=0.4667 \end{gathered}$

Number of people selected, n= 12;

$P(X=x)=^nC_x(p)^x(1-p)^{n-x}$

Thus, we have;

$\begin{gathered} P(X=12)=^{12}C_{12}(0.4667)^{12}(0.5333)^{12-12} \\ P(X=12)=1(1)(0.4667)^{12} \\ P(X=12)=0.0001 \end{gathered}$