Answer to Question #129233 in Statistics and Probability for Alia Aziz

Question

Three cooks Mohsin, Khurram, and Shahid bake a special kind of cake. In the restaurant where they work, Mohsin, bakes 55 percent of these cakes, Khurram bakes 25 percent and Shahid bakes 20 percent and with respective probabilities of 0.03, 0.02 and 0.05 they fail to rise. A cake is selected and fails to rise what is probability that it was backed by cook Khurram.

Answer 1

The probability that the picked cake fails to rise equals $0.03*0.55+0.02*0.25+0.05*0.2=0.0315.$

This means that 315 cakes out of 10000 fails to rise.

The probability that a picked cake fails to rise AND is baked by Khurram equals

$0.02*0.25=0.005.$

Thus 50 cakes out of 10000 fail to rise and are made by Khurram.

Hence if the picked cake fails to rise, the probability it was baked by khurram equals

$0.005/0.0315=0.159=15.9\%.$