An aerospace company has submitted bids on to separate ederal government de ense

Question

An aerospace company has submitted bids on to separate ederal government de ense contracts he compan pres en be rest at eres a probability o wining the r contract. If they win the first contract, the probability of winning the second s 72%, However, if they lose the irst contract the president th nk that the probability of winning the second contract decreases to 51%. A. What is the probability that they win both contracts? Probability B. What is the probability that they lose both contracts? Probability C. What is the probability that they win only one contract? Probability

Explanation / Answer

Here P(Winning the first contract) = 44%
If they win the first contract then P(Winning second contract) = 72%
If they lose the first contract then P(Winning second contract) = 51%

A) P(Winning both contracts) = P(Winning first contract) * P(Winning second contract given first contract is won) = 0.44 * 0.72 = 0.3168

B) P(losing both contracts) = P(Losing first contract) * P(Losing second contract given first contract is lost) = (1 - 0.44) * (1 - 0.51) = 0.2744

C) P(winning only one contract) = 1 - P(Winning both contracts) - P(Losing both contracts)
= 1 - 0.3168 - 0.2744 = 0.4088

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