Question: Use the information given in Problem 24 to find: (a) P(A 1 |E) (b) P(A 2 |E) (c) P(A 3 |E) Data from Problem 24

Use the information given in Problem 24 to find:

(a) P(A₁|E)

(b) P(A₂|E)

(c) P(A₃|E)

Data from Problem 24

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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