The ontime completion of Activity A in a construction projec

The on-time completion of Activity A in a construction project depends on the on-time completion of prior Activities B and C. If both B and C are completed on time, for sure A will be completed on time. If only one of the two Activities B and C are completed on time, A will have a 50 percent probability that it will be completed on time. If neither Activities B and C are completed on time, A will only have a 10 percent probability that it will be completed on time. From past experience, we know that Activities B and C each have an 80 percent probability to be completed on time. Activities B and C are independent. Compute the probability that Activity A will be completed on time. If we allow a delay in the completion of A, what is the probability that only Activity B is not completed on time?

Solution

(a)The probability that A will complete in time=P(B’)*P(C’)*P(A)+P(B)*P(C’)*P(A)+P(B’)*P(C)*P(A)

+P(B)*P(C)*P(A)=0.2*0.2*0.1+0.8*0.2*0.5+0.2*0.8*0.5+0.8*0.8*1

=0.804

(b)The probability that only activity B is not completed on time is: P(B’)*P(C)*P(A)/ P(B’)*P(C’)*P(A)+P(B)*P(C’)*P(A)+P(B’)*P(C)*P(A)

+P(B)*P(C)*P(A)=(0.2*0.8*0.5)/0.804=0.08/0.804=0.09