3. Given the following information, complete the tree diagram for a two-stage experiment with three outcomes X, Y, and Z in the first stage, and two outcomes a and b in the second stage: Pr[X] = 1/2, Pr[Xa] = 1/8, Pr[Xb) = 3/8, Pr[a|Y] = 1/4, Pr[b|Y] = 3/4, Pr[Ya] = 1/24, Pr[Yb) = 1/8, Pr[Za] = 1/6 %3D

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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3. Given the following information, complete the tree diagram for a two-stage experiment with three
outcomes X, Y, and Z in the first stage, and two outcomes a and b in the second stage: Pr[X] = 1/2,
Pr[Xa] = 1/8, Pr[Xb] = 3/8, Pr[a|Y] = 1/4, Pr[b|Y] = 3/4, Pr[Ya] = 1/24, Pr[Yb) = 1/8, Pr[Za] = 1/6.
Answer the following questions using your tree above:
(a) What is Pr[a|X]?
(b) What is Pr[Y]?
(c) What is the probability of b occurring given that Y has occurred?
Transcribed Image Text:3. Given the following information, complete the tree diagram for a two-stage experiment with three outcomes X, Y, and Z in the first stage, and two outcomes a and b in the second stage: Pr[X] = 1/2, Pr[Xa] = 1/8, Pr[Xb] = 3/8, Pr[a|Y] = 1/4, Pr[b|Y] = 3/4, Pr[Ya] = 1/24, Pr[Yb) = 1/8, Pr[Za] = 1/6. Answer the following questions using your tree above: (a) What is Pr[a|X]? (b) What is Pr[Y]? (c) What is the probability of b occurring given that Y has occurred?
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