Answer:
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
