Problem 8 (9 points) Events A.B,C are shown in the Venn Diagram below with proba

Question

Problem 8 (9 points) Events A.B,C are shown in the Venn Diagram below with probabilities labeled 0.15 0.06 0.19 0.03 0.05 0.07 Everything Else: prob: 0.35 0.10 Suppose you will earn $2 if event A happens $3 if event B happens . $5 if event C happens. So, potentially you could earn up to $10 total (if all 3 happen). 2pts | a) What is the chance you earn a total of exactly $10? O.0sS [ 3pts What is the chance you earn a total of exactly $5? CABnA 1165 Given that event C happened, what is the conditional probability you earn a total of exactly $8?10S 4pts 2

Explanation / Answer

a) P(A and B and C) = 0.03

b) P(C only) + P(A and B) - P(A and B and C) = 0.1 + 0.06 = 0.16

c) P(B|C) = ?

P(B|C) = P(B and C) / P(C)

P(B|C) = 0.07/0.25 = 7/25

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