Use the information given in Problem 23 to find (a) P(A 1 E) (b) P(A 2 E) (c) P(A 3 E) Data from Problem 23 Suppose that events A 1 , A 2 , and A 3 form a partition of the sample space S with P(A 1 ) 0 35, P(A 2 ) 0 45, and P(A 3 ) 0 2 If E is an event that is a subset of S and P(E A 1 ) 0 25, P(E ...

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Use the information given in Problem 23 to find: (a) P(A 1 |E) (b) P(A 2 |E)

Question:

Use the information given in Problem 23 to find:

(a) P(A₁|E)

(b) P(A₂|E)

(c) P(A₃|E)

Data from Problem 23

Suppose that events A₁, A₂, and A₃ form a partition of the sample space S with P(A₁) = 0.35, P(A₂) = 0.45, and P(A₃) = 0.2. If E is an event that is a subset of S and P(E|A₁) = 0.25, P(E|A₂) = 0.18, and P(E|A₃) = 0.14, find P(E).

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