In a building construction project, the on-time completion of the building requires the successive completion of a series of activities. Define E = excavation completed on time; and P[E] = 0.8 F = foundation completed on time; and P[F] = 0.7 S = superstructure completed on time; and P[S] = 0.9 Assume statistical independence among these events.

The probability of the completion of the project on time is 0.504.

Step-by-step explanation:

The question is:

Define the event C : (project completed on time) in terms of E, F and S. Compute the probability P(C) operations will not be on time in terms of E, F and S.

Solution:

The events are:

E = excavation completed on time; P [E] = 0.8

F = foundation completed on time; P [F] = 0.7

S = superstructure completed on time; P [S] = 0.9

The event C denotes the completion of the project on time.

Compute the probability of event C as follows:

P (C) = P (E ∩ F ∩ S)

        = P (E) × P (F) × P (S)

        = 0.8 × 0.7 × 0.9

        = 0.504

Thus, the probability of the completion of the project on time is 0.504.