Lesson A company bids on two separate contracts
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<H2>A company bids on two separate contracts</H2> <H3>Problem 1</H3>An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 57% probability of winning the first contract. If they win the first contract, the probability of winning the second is 67%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 44%. What is the probability that they lose both contracts? <B>Solution</B> Step by step. <pre> P(win 1st contract) = P(1) = 0.57 (given). P(lose 1st contract) = 1 - 0.57 = 0.43 (the complement). P(win 2nd contract) = P(2) = 0.57*0.67 + (1-0.57)*0.44 = 0.5711. P(win both 1st and 2nd contracts) = 0.57*0.67 = 0.3819. P(win at least one of the two contracts) = P(1) + P(2) - P(both) = 0.57 + 0.5711 - 0.3819 = 0.7592. P(lose both) = 1 - P(win at least one of the two contracts) = 1 - 0.7592 = 0.2408. <U>ANSWER</U> </pre> <H3>Problem 2</H3>A contract company has bid on two contracts. The probability of winning contract A is 0.71. If the company wins contracts A, the probability of winning contract B is 0.62. If the company loses contract A, the probability of winning contract B decreases to 0.33. What is the probability of not winning any contract? <B>Solution</B> Step by step. <pre> (a) P(A win) = 0.71 (given). (b) P(both A and B win) = 0.71*0.62 = 0.4402. (c) P(B win) = 0.71*0.62 + (1-0.71)*0.33 = 0.5359. (d) P(A or B win) = P(A win) + P(B win) - P(both A and B win) = 0.71 + 0.5359 - 0.4402 = 0.8057. 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