The accompanying tree diagram represents a two-stage experiment. (Let x = 0.45, y = 0.55, r = 0.65, s = 0.35, t = 0.4, and w = 0.6.)

Question

Use the diagram to find the following probabilities. (Round your answers to three decimal places.)
(a) Find P(A) · P(D | A).


(b) Find P(B) · P(D | B).


(c) Find P(A | D).

Answer 1

(a) P(A) · P(D | A) = 0.450 · 0.400 = 0.180
(b) P(B) · P(D | B) = 0.550 · 0.600 = 0.330
(c) P(A | D) = P(A) · P(D | A) / [P(A) · P(D | A) + P(B) · P(D | B)] = 0.180 / (0.180 + 0.330) = 0.353