Answer to Question #176961 in Statistics and Probability for Sean

Question

1.2 It has been established that completion of construction projects can be delayed because of 

unfavourable weather conditions. The probabilities are 0.6 that there will be unfavourable 

weather, and 0.85 that the construction project will be completed on time if the weather is 

favourable and 0.35 that the construction project will be completed on time if there is 

unfavourable weather. 

Required:

What is the probability that the construction project will not be completed on time? (10)

Question II [25]

Answer 1

Solution:

Notations:

U = unfavourable weather

F = favourable weather

C = work completed

Given, P(U) = 0.6, P(C|F) = 0.85, P(C|U) = 0.35

So, P(C) = 1-0.6 = 0.4

Now, P(C) = P(U)P(C|U) + P(F)P(C|F) = 0.6 x 0.35 + 0.4 x 0.85 = 0.55

Then, P(C') = 1-P(C) = 1-0.55 = 0.45