- #1

TheClincher

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## Homework Statement

A contractor has two subcontractors for his excavation work. Experience shows that in 60% of the time, subcontractor A was available to do a job, whereas subcontractor B was available 80% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time.

a) Probability that both subcontractors will be available to do the next job.

b) If contractor learned that subcontractor A is not available for the job, what is the probability that the other subcontractor will be available?

## Homework Equations

A = sub A available

B = sub B available

## The Attempt at a Solution

a) P(AB) = P(A)P(B)

b is the one I have a question on. I think it's the following set up but I don't know how to continue or what to do with it:

b) P(B|[tex]\bar{A}[/tex]) = P(B[tex]\bar{A}[/tex])/P([tex]\bar{A}[/tex])

Okay uhh I don't know if this is sensible but I took P(B[tex]\bar{A}[/tex]) and did the following

P(B[tex]\bar{A}[/tex]) = 1-complement of P(B[tex]\bar{A}[/tex]) and expanded it to get 0.32. So if I plug that into P(B|[tex]\bar{A}[/tex]) = P(B[tex]\bar{A}[/tex])/P([tex]\bar{A}[/tex]) I got 0.32/0.40 = 0.80. Eh? Can someone steer me right

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