# two step probability problem

**Question description**

kl trucking is starting a project designed to increase the generating capacity of one of its plants in northern Kentucky. The project is divided into two sequential stages or steps: stage 1 (design) and stage 2 (construction). While each stage will be scheduled and controlled as closely as possible, management cannot predict beforehand the exact time required to complete each stage of the project. An analysis of similar construction projects has shown completion times for the design stage of 2, 3, or 4 months with respective probabilities of .2, .5, and .3, and completion times for the construction stage of 6, 7, or 8 months with respective probabilities of .1, .4 and .5

Find the probability that the project will be completed in:

a) 8 months

b) 10 months

c) 12 months

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