An aeroplane company has submitted bids on two separate federal government defen

Question

An aeroplane company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract , the probability of winning the second is 65%. However, if they lose the first contract the president thinks that the probability of winning the second contract decreases to 53%.

a.What is the probability that they win both contracts?

b.What is the probability that they lose both contracts?

c.What is the probability that they win only one contract?

Explanation / Answer

P(winning first) = 0.44

P(winning second | win first) = 0.65

P(winning second | lose first) = 0.53

a) P(winning both the contracts) = P(winning second | win first) * P(win first) = 0.65 * 0.44 = 0.286

b) P(winning second) = P(winning second | win first) * P(win first) + P(winning second | lose first) * P(lose first)

                                   = 0.65 * 0.44 + 0.53 * (1 - 0.44)

                                   = 0.5828

P(winning. at least one contract) = P(winning first) + P(winning second) - P(winning both)

                                                     = 0.44 + 0.5828 - 0.286

                                                     = 0.7368

P(loosing both the contracts) = 1 - P(winning. at least one contract) = 1 - 0.7368 = 0.2632

c) P(win only one contract) = P(win only first) + P(win only second)

                                            = P(win first) - P(win both) + P(win second) - P(win both)

                                            = 0.44 - 0.286 + 0.5828 - 0.286

                                            = 0.4508

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