Homework SourseUse Bayes theorem or a tree diagram to calculate the indicat
Use Bayes\' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]
Y1, Y2, Y3 form a partition of S. P(X | Y1) = .4, P(X | Y2) = .4, P(X | Y3) = .2, P(Y1) = .3, P(Y2) = .2.
Find P(Y1 | X).
Solution
P(Y1/X)=(P(Y1)P(X/Y1))/(P(Y1)P(X/Y1)+P(Y2)P(X/Y2)+P(Y3)P(X/Y3))=(0.3×0.4)/((0.3×0.4)+(0.2×0.4)+(0.5×0.2))=0.4
![Use Bayes\' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.] Y1, Y2, Y3 form a](/WebImages/30/use-bayes-theorem-or-a-tree-diagram-to-calculate-the-indicat-1084591-1761570072-0.webp "Use Bayes\' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.] Y1, Y2, Y3 form a")
