Two firms X and Y consider bidding on a road-building job, which may or may not

Question

Two firms X and Y consider bidding on a road-building job, which may or may not be awarded depending on the amounts of the bids. Firm X submits a bid and the probability is 1/3 that firm X will get the job provided firm Y does not bid. The probability is 3/4 that Y will bid and if it does, the probability that X will get the job is only 1/4. (a) What is the probability that X will NOT get the job? (b) If X does not get the job, what is the probability that Y did bid? (c) If X does get the job, what is the probability that Y did NOT bid?

Explanation / Answer

Ans: P(X get Job/Y does not bid)=1/3

P(X does not get Job/Y does not bid)=1-1/3=2/3

P(X get job/Y bid)=1/4

P(X does not get Job/Y bid)=1-1/4=3/4

P(Y bid)=3/4,

P(Y does not bid)=1/4

a)

P(X get job)=P(X get Job/Y bid)*P(Y bid)+P(X get Job/Y does not bid)

=1/4*3/4+1/3*1/4

=3/16+1/12=0.2708

b)P(Y bid/X does not get Job)

=P(X does not get Job/Y bid)*P(Y bid)/[P(X does not get Job/Y bid)*P(Y bid)+P(X does not get Job/Y does not bid)*P(Y does not bid)

=3/4*3/4/[3/4*3/4+2/3*1/4]

=9/16/[9/16+2/12]

=0.5625/0.7292

=0.7714

c)P(Y does not bid/X get Job)

=P(X get Job/Y does not bid)*P(Y does not bid)/[P(X get Job/Y does not bid)*P(Y does not bid)+P(X get Job/Y bid)*P(Y bid)

=1/3*1/4/[1/3*1/4+1/4*3/4]

=1/12/[1/12+3/16]

=0.3077

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