Successful completion of a construction project depends on the supply of materials and labor as well as the weather condition. Consider a given project that can be success fully completed if either one of the following conditions prevails:

(a) Good weather and at least labor or materials are adequately available.

(b) Bad weather but both labor and materials are adequately available.

Define:

G = Good weather

G = Bad weather

L = Adequate labor supply

M = Adequate materials supply

C = successful completion

Suppose P(L) = 0.7: P(G) = 0.6 and L is independent of both M and G. If the weather is good, adequate supply of materials is guaranteed, whereas the probability of adequate supply of material is only 50% if bad weather prevails.

(a) Formulate the event of successful completion in terms of G, L. and M.

(b) Determine the probability of successful completion.

(c) If the project was successfully completed, what is the probability that labor supply and been inadequate?