Question
Asked Feb 26, 2020
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the first outcome is one of X and Y the second outcome is one of A and B if the first outcome is X, and one of A, B, and C if the first outcome is Y. 

Pr[X]=0.4Pr[X]=0.4
Pr[Y]=0.6Pr[Y]=0.6
Pr[A|X]=0.5Pr[A|X]=0.5
Pr[B|X]=0.5Pr[B|X]=0.5
Pr[A|Y]=0.3Pr[A|Y]=0.3
Pr[B|Y]=0.2Pr[B|Y]=0.2
Pr[C|Y]=0.5

(1) Pr[A]=

(2) Pr[X|A]=Pr[X|A]= 

(3) Pr[Y|B]=

(4) Pr[B|Y]=

 

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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

1) The first outcome can occur in 2 ways, X or Y.

Probability homework question answer, step 1, image 1

Step 2

2) Use Bay's theorem:

Probability homework question answer, step 2, image 1

Answer: 0.5

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