Two firms V and W consider building on a road building job which may or may not

Question

Two firms V and W consider building on a road building job which may or may not be awarded depending on the amounts of the bids. Firm V submits a bid and the probability is 3/4 that it will get the job provided firm W does not bid. The odds are 3 to 1 that W will bid, and, if it does, the chance that V will get the job is only 1/3, what is the probability that V will get the job? Note: the odds that on event will occur are given by the ratio of the probability that the event will occur to the probability that it will not occur (assuming to the neither is you). Show that if the odds are a to b that an event will occur, its probability is a/a+b.

Explanation / Answer

Let A:V gets the project

B: W gets the project

Given P(A/B complement)=3/4

P(B)=3/4

P(A/B)=1/3

We need to find P(A)

Using Bayes theorem

P(A)=P(A/B)*P(B)+P(A/B complement)*P(B complement)

=1/3*3/4+3/4*(1-1/4)=0.4375

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