3.35 With probability 0.6, the present was hidden by mon;with probability 0.4, i

Question

3.35 With probability 0.6, the present was hidden by mon;with probability 0.4, it was hidden by dad. When mom hidesthe present, she hides it upstairs 70 percent of the time anddownstairs 30 percent of the time. Dad is equally likely tohide it upstairs r downstairs. a) What is the probability that the present isupstairs? b) Given that it is downstairs, what is the probabilityit was hidden by dad? 3.35 With probability 0.6, the present was hidden by mon;with probability 0.4, it was hidden by dad. When mom hidesthe present, she hides it upstairs 70 percent of the time anddownstairs 30 percent of the time. Dad is equally likely tohide it upstairs r downstairs. a) What is the probability that the present isupstairs? b) Given that it is downstairs, what is the probabilityit was hidden by dad?

Explanation / Answer

All the possibilities are: the present was hidden by mom and hidden downstairs, P =.6*.3 = .18 the present was hidden by mom and hidden upstairs, P =.6*.7 = ..42 the present was hidden by dad and hidden downstairs,P = .4*.5 = .2 the present was hidden by dad and hidden upstairs,P = .4*.5 = .2 A) Probability that it was hiddne upstairs = .42+.2 = .62 or62% B) the total probability that it was hidden dowstairs = .18+.2= .38 and the probability that if it was hidden downstairs it washidden by dad = .2/.38 ˜.5263 or ˜ 52.63%

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