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

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## Description

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.
2. You have been assigned to estimate the cost of installing fiber optic cable in a country. Fortunately, you have done a number of similar projects in this area in the past and you have accumulated the following parametric cost estimates based on this experience:

Mobilization/demobilization Cost = \$10,000

Buried cable construction:
Cost per kilometer = \$10,000 Sand
Cost per kilometer = \$17,500 Sand & Clay
Cost per 100 meters = \$ 5,500 Rock

Cost per kilometer = \$ 7,500

Cost per Road Crossing = \$12,500
Cost per pipeline Crossing = \$ 5,000

The scope of the new project is as follows:

Predominately sand 150 km
Predominately sand & clay 100 km
Rock 500 meters