2. Suppose that the probability it rains tomorrow is p. Given that it rains tomo

Question

2. Suppose that the probability it rains tomorrow is p. Given that it rains tomorrow, the probability I bring an umbrella to school that day is a. Given that it does not rain tomorrow, the probability I bring an umbrella to school that day is B. a) (Epts) Find the probability that it rains tomorrow and I do not bring an umbrella to school. (b) (10pts) Find the probability that I bring an umbrella to school. (c) (10pts) Given that I do not bring an umbrella to school tomorrow, what is the probability that it rains that day. (Note, answers should be in terms ofp, and )

Explanation / Answer

(a) P(Rain and No Umbrella) = p - p  = p(1 - )

(b) P(Umbrella) = p( + )

(c) P(Rain | No Umbrella) = P(Rain and No Umbrella)/P(No Umbrella)

= (p - p) / [1 - p( +)]

= [p(1 - ) /  [1 - p( +)]

Umbrella No Umbrella Total Rain p p - p p No Rain p 1 - p - p 1 - p Total p( + ) 1 - p( + ) 1

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