Question

o firms V and W consider bidding on a road building job, which may or may not be awarded de- pending on the amounts of the bids. Firm V submits a bid and the probability is 0.8 that it will get the job provided firm W does not bid. The probability is 0.7 that W will bid, and if it does, the probability that V will get the job is only 0.4. (a) What is the probability that V will get the job? (b) If V gets the job, what is the probability that W did not bid?

Answer 1

The probability that V gets the job given that W does not bid is P(V|W') = 0.8

The probability that W will bid, P(W) = 0.7

The Probability that V will get the job given that W will bid is P(V|W) = 0.4

a) The probability that V will get the job is

Using Bayes Theorem ,

P(V) = P(V|W)*P(W)+P(V|W')*)(W')

=0.4*0.7+0.8*0.3 =0.28+0.24 =0.52

Answer: P(V) = 0.52

b) The probability that V gets the job nad W did not bid is P(W'|V)

$P(V\cap W)= P(V|W)*P(W)= 0.4*0.7 =0.28$

$P(W|V) = \frac{ P(V\cap W)}{P(V)} = \frac{0.28}{0.52} =0.5385$

And,