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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 −  =

Question

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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Solution

0.15 = 0.65. Therefore, the probability of either event A or event B occurring is 0.65.

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