Suppose that events A 1 , A 2 , and A 3 form a partition of the sample space S with P(A 1 ) 0 3, P(A 2 ) 0 65, and P(A 3 ) 0 05 If E is an event that is a subset of S and P(E A 1 ) 0 05,P(E A 2 ) 0 25, and P(E A 3 ) 0 5, find P(E)

Question: Suppose that events A 1 , A 2 , and A 3 form a partition of the sample space S with P(A 1 ) =

Suppose that events A₁, A₂, and A₃form a partition of the sample space S with P(A₁) = 0.3, P(A₂) = 0.65, and P(A₃) = 0.05. If E is an event that is a subset of S and P(E|A₁) = 0.05,P(E|A₂) = 0.25, and P(E|A₃) = 0.5, find P(E).

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