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=(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}`