Answer to Question #69783 in Statistics and Probability for JItender

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

Let the event “there will be a strike” is A, the event “the construction will be completed on time” is B.
P(A)=0.7
P(B|A ̅ )=0.9
P(B|A)=0.4
P(B)=P(A)P(B|A)+P(A ̅ )P(B|A ̅ )=P(A)P(B|A)+(1-P(A))P(B|A ̅ )
P(B)=(0.7)0.4+(1-0.7)0.9= 0.55
Answer: 0.55.