Sample space s is partitioned into E_1 and E_2 such that P(E_1) = 0.40 and P(E_2

Question

Sample space s is partitioned into E_1 and E_2 such that P(E_1) = 0.40 and P(E_2) = 0.50. Let D be an event such that P(D|E_1) = 0.35 and P(D|E_2) = 045. a) Find P(D) and P(D') b) Find P(E_1|D) and P(E_1|D'). c) Find P(E_2|D) and P(E_2|D') a) P(D) = (Round to three decimal places as needed.) P(D') = (Round to three decimal places as needed.) b) P(E_1|D) = (Round to three decimal places as needed.) P(E_1|D') = (Round to three decimal places as needed.) c) P(E_2|D) = (Round to three decimal places as needed.) P(E_2|D') = (Round to three decimal places as needed.)

Explanation / Answer

a) P(D) = 0.35*0.40+0.45*0.60 = 0.410

P(D') = 1-0.410 = 0.590

b) P(E1|D) = (0.35*0.40)/0.41 = 0.341

P(E1|D') = (0.65*0.40)/0.59 = 0.441

c) P(E2|D) = (0.45*0.60)/0.41 = 0.659

P(E2|D') = (0.55*0.60)/0.59 = 0.559

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