A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.60, and the probability that a shopper buys cheese is 0.20.Event A = A shopper buys bread.Event B = A shopper buys cheese.A and B are independent events if _____.A.the probability of buying bread or cheese is 0.12B.the probability of buying bread and cheese is 0.12C.the probability of buying bread and cheese is 0D.the probability of buying bread or cheese is 0.80
Question
A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.60, and the probability that a shopper buys cheese is 0.20.Event A = A shopper buys bread.Event B = A shopper buys cheese.A and B are independent events if _____.A.the probability of buying bread or cheese is 0.12B.the probability of buying bread and cheese is 0.12C.the probability of buying bread and cheese is 0D.the probability of buying bread or cheese is 0.80
Solution
Events A and B are independent if the probability of both events occurring is the product of the probabilities of each event occurring individually.
In this case, Event A is a shopper buying bread, which has a probability of 0.60, and Event B is a shopper buying cheese, which has a probability of 0.20.
If A and B are independent, the probability of both A and B occurring (i.e., a shopper buying both bread and cheese) would be the product of the probabilities of A and B, which is 0.60 * 0.20 = 0.12.
Therefore, A and B are independent events if the probability of buying bread and cheese is 0.12. So, the correct answer is B. the probability of buying bread and cheese is 0.12.
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