Suppose that a, b, and c are three independent events such that pr(a) = 1/4, pr(b) = 1/3, and pr(c) = 1/2. (a) determine the probability that none of these three events will occur. (b) determine the probability that exactly one of these three events will occur.

a) 1/4

b) 11/24

Step-by-step explanation:

A, B, and C are three independent events.

Considering Pr(A'), Pr(B') and Pr(C') probabilities of not occoring A, B and C, so:

Pr(A) = 1/4 Pr(A') = 3/4

Pr(B) = 1/3 Pr(B') = 2/3

Pr(C) = 1/2 Pr(C') = 1/2

(a) Determine the probability that none of these three events will occur.

Pr(A') * Pr(B') * Pr(C') = 3/4 * 2/3 * 1/2 = 1/4

(b) Determine the probability that exactly one of these three events will occur.

exactly one means:

1) A occur B not occur and C not occur OR

2) A not occur B occur and C not occur OR

3) A not occur B not occur and C occur. So,

1) 1/4*2/3*1/2 = 1/12

2) 3/4*1/3*1/2 = 1/8

3) 3/4*2/3*1/2 = 1/4

1/12 + 1/8 + 1/4 = 11/24