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# There are three (and only three) paths through a network (project), Resolved

There are three (and only three) paths through a network (project),
Resolved Question:
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.
What is the probability the project being completed in 24 months or longer.

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Customer: replied 3 years ago.

In your explanation you state "the project would be completed within 24 months if any of the three paths is completed within 24 months". For the project to be complete all paths must be completed within 24 months.

Would not the equation be (.95)*(.90)*(.85)?

No, because that equation would mean that all three paths must be completed within 24 hours. Since all activities (therefore paths) are independent, project can be completed along any path irrespective of whether rest of the activities are complete or not. So, project is complete if any of the three paths is complete.

So, the answer is 'any path', not 'all paths'
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