0-72.5 points waneFMAC7 8 6 002. Use Bayes\' theorem or a tree diagram to calcul
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Question
0-72.5 points waneFMAC7 8 6 002. Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.] P(B | A)-l 2. 0-112.5 points waneFMACT 8 6 003 Use Bayes' theorem or a tree diagram to e the indicated probability. Round your answer to four decimal places. HINT [See Example 3.] 3. -12.5 points WaneFMACT 8.6.006 Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]Explanation / Answer
1)
P(A/B) = P(A?B)/P(B)
0.7 = P(A?B)/0.3
P(A?B) = 0.21 => 1
P(A/B’) = P(A?B’)/P(B’)
0.6 = P(A?B’)/0.7
P(A?B’) = 0.42 =>2
P(A) = P(A?B)+ P(A?B’) = 0.21+0.42 = 0.63
P(B/A) = P(A?B)/P(A)
= 0.21/0.63 = 0.3333
2)
P(X/Y’) = P(X?Y’)/P(Y’)
0.7 = P(X?Y’)/0.5
P(X?Y’) = 0.35 => 1
P(X/Y) = P(X?Y)/P(Y)
0.2 = P(X?Y)/0.5 {P(Y) = 1-P(Y’) = 0.5}
P(X?Y) = 0.1 => 2
P(X) = P(X?Y)+ P(X?Y’) = 0.35+0.1 = 0.45
P(Y/X) = P(X?Y)/P(X)
P(Y/X) = 0.1/0.45 = 0.2222
3)
P(X/Y1) = = P(X?Y1)/P(Y1)
0.6= P(X?Y1)/0.3
P(X?Y1) = 0.18
P(X/Y2) = P(X?Y2)/P(Y2)
0.3 = P(X?Y2)/0.2
P(X?Y2) = 0.15
P(X/Y3) = = P(X?Y3)/P(Y3)
0.1= P(X?Y3)/0.5 {as P(Y3) = 1 – P(Y1) – P(Y2)}
P(X?Y3) = 0.05
P(X) = P(X?Y1)+ P(X?Y2)+ P(X?Y3)
P(X) = 0.18+0.15+0.05 = 0.38
P(Y1/X) = P(X?Y1)/P(X)
= 0.18/0.38 = 0.4737
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