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Chuck is a fool with probability 0.6, a thief with probability 0.7, and neither with probability...

Chuck is a fool with probability 0.6, a thief with probability 0.7, and neither with probability 0.25. a. What is the probability that he is a fool or a thief but not both? b. What is the conditional probability that he is a thief, given that he is not a fool?

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Answer #1

What is the probability that he is a fool or a thief but not both?

n Let A be the event that Joe is a fool and B be the event that Joe is a thief. We are given that Pr(A) = 0.6

Pr(B) = 0.7

Pr (A ∪ B) c = 0.25

Pr (A UB)-1- Pr ((AUB)) 0.75 Pr(A n B) = Pr(A) + Pr(B) _ Pr(A U B) 0.55 The event that he is a fool or a thief but not both is given by (An Bc) U (Ac nB). Looking at the Venn diagram, the probability should be We can also derive this as follows Thus, Pr ((AUB) n (An B)) = Pr(AUB) + Pr ((AnB))-Pr ((AUB) U.(An B)) = Pr(AUB) + 1-Pr(An B)--Pr(s)

b. What is the conditional probability that he is a thief, given that he is not a fool?

e need to finc Pr( BIA ) PrIA 0.7+0.55 = o.375

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