Question: Problem 2.12 Given P(A1)=0.5, P(A2)=0.4, P(A3)=0.4, P(A1 A2) = .04, P(A1 A3)=0.1, P(A2 A3)=0.2, P(A1 A2 A3)=0.02. Using this information,

Problem 2.12 Given P(A1)=0.5, P(A2)=0.4, P(A3)=0.4, P(A1 ∩ A2) = .04, P(A1 ∩ A3)=0.1, P(A2 ∩ A3)=0.2, P(A1 ∩ A2 ∩ A3)=0.02. Using this information, Venn diagrams, and Propositions 2.1 and 2.5 compute the following probabilities:

(a) P(A1 ∪ A2 ∪ A3)

(b) P(A 1 ∩ A 2 ∩ A 3)

(c) P((A1 ∪ A2) ∩ A3)

(d) P((A1 ∪ A2) ∩ A 3)

(e) P(A 1 ∩ A2 ∩ A3)

(f) P(A 1 ∩ A 2 ∩ A3)

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