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