Your company is submitting bids for two different projects, project A and projec

Question

Your company is submitting bids for two different projects, project A and project B. Based on their research, your company experts estimate that the probability of winning the bid for project A is 0.28 and the probability of winning the bid for project B is 0.42. Their research has also shown that if the company wins one bid, the chance of winning the other bid is reduced to half of the original probability. Using this information, answer the following questions: What is the probability of winning both bid projects? What is the probability of winning at least one of the bids?

Explanation / Answer

P(Winning A) = 0.28, Therefore P(Not winning A) = 1-0.28 = 0.72

P(Winning B) = 0.42, Therefore P(Not winning B) = 1-0.42 = 0.58

(a) P(Winning Both Projects) = P(Winning A first then B) + P(Winning B first, then A)

P(Winning A first and then B) = 0.28 * (0.5*0.42) = 0.0588

P(Winning B First and then A) = 0.42 * (0.5*0.28) = 0.0588

Therefore the required probability = 0.0588 + 0.0588 = 0.1176

(b) Probability of winning at least one bid = P(Winning both) + P(Winning A, losing B) + P(Losing A, winning B) = 1 - P(Not winning any bids) [ since sum of probabilities = 1]

P(Not winning any Bid) = P(Losing A and losing B) = 0.72*0.58 = 0.4176

Therefore P(Winning at least 1 bid) = 1 - 0.4176 = 0.5824

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