The probability that Firm X can either submit or not submit adesign for a bid fo

Question

The probability that Firm X can either submit or not submit adesign for a bid for the construction job is 1/2. In eitherevent, Firm Y, also biding for the job, could or could not win thebid. If Firm X does not bid, the probability the Firm Y willget the job is 2/3. If Firm X does bid, the probability thatFirm Y will win the job is 1/5. Find the following:
a. If Firm Y wins the job, what is the probability that FirmX bid?
b. If Firm Y wins the job, what is the probability that FirmX did not bid?
c. If Firm Y does not win the job, what is the probabilitythat Firm X bid?
d. If Firm Y does not win the job, what is the probabilitythat Firm X did not bid?

Explanation / Answer

P Y, given not X = 2/3. P Y given X = 1/5. Ywins 2/3 x 1/2 plus 1/5 x 1/2 = 43% of the time (.33 +.10), Y loses 1/3 x 1/2 plus 4/5 x 1/2 = 57% (17+40) Xwins 1/2 x 4/5 = 40% NOTE THAT SOMETIMES X DOES NOT BID BUT Y DOES NOT WIN< SOTOTAL IS LESS THAN 100%    X bids Xno BID Xwins    Ywins    50% 50%
a. If Firm Y wins the job, what is the probability that FirmX bid? 10/43
b. If Firm Y wins the job, what is the probability that FirmX did not bid? 33/43
c. If Firm Y does not win the job, what is the probabilitythat Firm X bid? 40/57
d. If Firm Y does not win the job, what is the probabilitythat Firm X did not bid? 17/57

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