Solve the problem using Bayes Theorem Round the answer to th

Solve the problem using Bayes\' Theorem. Round the answer to the nearest hundredth, if necessary. 25) For mutually exclusive events X_1, X_2, and X_3, let P(X_1) = 0.54, P(X_2) = 0.15, and P(X_3) = 0.31. Also, P(Y_1X_1) = 0.40,P(Y_1X_2) = 0.30, and P(Y_1X_3) = 0.60 Find P (X2Y). A) 0.42 B) 0.20 C) 0.48 D.0.10

Solution

ACCORDING TO BAYES THEOREM,

p(X2/Y) = P(X2).P(Y/X2) / [ P(X1).P(Y/X1) +  P(X2).P(Y/X2) +   P(X3).P(Y/X3) ]

=> 0.15*0.30 / [ 0.54* 0.40 +0.15*0.30 +0.31*0.60 ]

=> 0.1786

=> B) 0.20