Each morning coffee is prepered for the entire office staff by oneo f the three

Question

Each morning coffee is prepered for the entire office staff by oneo f the three employees, denpending on who first arrives at work. Veronica arrives first 20% of the time; Gita and Mike are each the first to arrive on half of the remaining mornings. The probability that the coffee is bitter (not testing good) when Veronica prepares it is 0.1, while the corresponding probabilities when Gita and Mike prepare it are 0.2 and 0.3 respectively.

a) if you arrive one morning and find the coffee bitter, what is the probability that it was prepared by Veronica?

b) What is the probability that the coffee wil not be bitter on a given morning?

Explanation / Answer

a)

P(Coffee is bitter) =P(B) = 0.2*0.1 + 0.4*0.2+ 0.4*0.3 = 0.02+0.08+0.12 = 0.22

P(bitter Coffee is Prepared by Veronica) = P(V|B) = P(V n B)/P(B) = 0.2/0.1/0.22 = 0.02/0.22 = 0.09

b) P(coffee is not bitter on a given morning) = 1- 0.22 = 0.78

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