Three cooks, A, B, and C, bake a special kind of cake, and with respective proba

Question

Three cooks, A, B, and C, bake a special kind of cake, and with respective probabilities 02, 03, and 05, it fails to rise. In the restaurant where they work, cook A bakes 50 percent of these cakes, B bakes 30 percent, and C bakes 20 percent. (a) What is the probability that a randomly chosen cake will rise? Answer: (b) Given that a randomly chosen cake fails to rise, what is the conditional probability that it was baked by cook C? Answer: Consider the experiment of throwing two fair dice. Let A be the event that the sum of the two dice is 8, and let B be the event of rolling doubles. Are events A and B independent? Justify your answer.

Explanation / Answer

4 a) P(Cake will rise)

= P(Rise | A)*P(A) + P(Rise | B)*P(B) + P(Rise | C)*P(C)

= 0.98*0.5 + 0.97*0.3 + 0.95*0.2

= 0.971

b) P(C | Rise)

= P(C and Rise) / P(Rise)

= P(Rise |C)*P(C) / P(Rise)

= 0.95*0.2/0.971

= 0.1957 [Rounded off to 4 decimal places]

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