Answer to Question #65534 in Statistics and Probability for Kriti

Question

The construction of a building may be delayed by a strike. Suppose that the
probability that there will be a strike is 0.70, the probability that the construction
will be completed on time if there is no strike is 0.90 and the probability that the
building will be completed on time if there is a strike is 0.40, what is the
probability that the construction will be completed on time.

Answer 1

P(A) is the probability that the construction will be completed on time;
P(H1)is the probability that there will be a strike;
P(H2) is the probability that there will not be a strike;
P(H1/A) is the probability that the construction will be completed on time if there is no strike;
P(H2/A) is the probability that the building will be completed on time if there is a strike.

By the condition of the problem we have that
P(H1) = 0.70,
P(H2) = 1 - P(H1) = 1 - 0.70 = 0.30,
P(H1/A) = 0.90,
P(H2/A) = 0.40.

Then
P(A) = P(H1)P(H1/A) + P(H2)P(H2/A) = 0.700.90 + 0.300.40 =
= 0.63 + 0.12 = 0.75