Joe wants to purchase a particular model of automobile. There are three dealers

Question

Joe wants to purchase a particular model of automobile. There are three dealers that Joe is considering. The probability that Joe will go to dealer one is 0.30, the probability that Joe will go to dealer two is 0.40 and the probability that Joe will go to dealer three is 0.30;   At dealer one the probability of buying this particular model is 0.35, at dealer two the probability of buying this particular model is 0.45, and at dealer three the probability of buying this particular model is 0.20; you have learned that Joe purchased this particular model, what is the probability that Joe purchased it at dealer one?

Explanation / Answer

P(Joe purchased the product at dealer one) = P(Joe went to dealer one and he will that particular model) = 0.3 * 0.35 = 0.105. (Ans).

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