1There are three and only three paths through a network proj

1.There are three (and only three) paths through a network (project), each with a probability of completion in less than 24 months as indicated:

a.S-a-b-F           P₁(<24) = .95

b.S- d-e-F          P₂(<24) = .85

c.S- g-h-F          P₃(<24) = .90

If the tasks are independent, what is the probability of the network being completed within 24 months? Note: S is the start node, F is the finish node.

Solution

Network will be completed if either of the three path completed.

Let us first find the probability that neither of the three path will complete. So

P(no path is completed within 24 months)=(1-0.95)*(1-0.85)*(1-0.90)=0.00075

So the probability that network being completed within 24 hours is

P(network completed in 24 months)=1- P(no path is completed within 24 months)=1-0.00075=0.99925

Hence, the required probability is 0.99925.