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A pet store sells mice, reptiles, and birds.Let event A = A customer buys a mouse.Let event B = A customer buys a bird.What does P(A or B) = 0.15 mean in terms of this problem?A.The probability that a customer buys neither a mouse nor a bird is 15%.B.Buying a mouse and buying a bird are mutually exclusive events.C.The probability that a customer buys both a mouse and a bird is 15%.D.The probability that a customer buys either a mouse or a bird is 15%.SUBMITarrow_backPREVIOUS

Question

A pet store sells mice, reptiles, and birds.Let event A = A customer buys a mouse.Let event B = A customer buys a bird.What does P(A or B) = 0.15 mean in terms of this problem?A.The probability that a customer buys neither a mouse nor a bird is 15%.B.Buying a mouse and buying a bird are mutually exclusive events.C.The probability that a customer buys both a mouse and a bird is 15%.D.The probability that a customer buys either a mouse or a bird is 15%.SUBMITarrow_backPREVIOUS

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Solution

D. The probability that a customer buys either a mouse or a bird is 15%.

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We found that P(A and B) = 0.15. Since the probability that both events happen at the same time is not 0, it means that events A and B have some outcomes in common. Therefore, the events A and B are not mutually exclusive.To compute P(A or B) means that we wish to find the probability that either A happened or B happened. Since the events are not mutually exclusive, we can apply the general addition rule for events. Recall that P(A) = 0.3 and P(B) = 0.5.P(A or B)  =  P(A) + P(B) − P(A and B) =  0.3 + 0.5 −  =

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