A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that construction hob will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

Explanation

A = The Construction job will be completed on time P(A) = ?
B = There is a strike
P(B) = 0.65 , P(A/B) = 0.80
.
P(A/B) = 0.32
.
P(A) = P(B) × P(A/B) + P(B′) × P(A/B′)
.
= 0.65 × 0.32 + (1−0.65) × 0.80
.
= 0.208 + 0.28
.
P(A) = 0.488 .