3. There is a 55% chance that firm A will bid for the construction of a new buil

Question

3. There is a 55% chance that firm A will bid for the construction of a new building. A second firm (firm B) submits a bid regardless. If firm A does not bid, there is a 2/3 chance that firm B will wirn the bid. If firm A does bid, there is a 1/5 chance that firm B will win the bid. (a) What is the probability that firm A bid and firm B did not win the bid? (b) If firm B won the bid, what is the probability that firm A did not bid? (c)If firm B did not win the bid, what is the probability that firm A bid?

Explanation / Answer

(a) Probability that A bids = 55/100

Probability that B win given A bids = 1/5

Probability A bids and B does not win = 55/100*4/5 = 0.44

(b) probability A does not bid given that B wins = probability A does not bid and B wins / prob ability B wins = (45/100 × 2/3 )/(45/100*2/3 + 55/100*1/5) = 0.7317

(c) probability A bids, given that B does not win = (55/100 * 4/5) / (55/100*4/5 + 45/100*1/3) = 0.7457

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