Question

math

2. Suppose that a jury of 12 persons is to be selected from a pool of 25 persons who were called for jury duty. The pool comprises 12 retired persons, 6 employed persons, 5 unemployed persons, and 2 students Assuming that each person is equally likely to be selected, answer the following: (a) What is the probability that both students will be selected? (b) What is the probability that the jury will contain exactly twice ersons as emplove

Answer 1

No of ways 12 persons can be selected from 25, N = 25C12

(a)

2 students will be picked up and rest 10 people will be picked from 23 people (12 retired, 6 employed and 5 unemployed). So the number of ways are, A = 2C2 * 23C10 = 23C10

Desired Probability, P(A) = 23C10 / 25C12 = 0.22

(b)

The possible ways are:

1. 2 employed and 4 retired (rest 6 from 7: 5 unemployed and 2 students )

2. 3 employed and 6 retired (rest 3 from 7: 5 unemployed and 2 students )

3. 4 employed and 8 retired

Number of ways are, B = 6C2 * 12C4 * 7C6 + 6C3 * 12C6 * 7C3 + 6C4 * 12C8 * 7C0

Desired Probability, P(B) = B / N = 0.1358

** If the answers do not match please comment