Solve the Problem Using Bayes' Theorem $X_{1}, X_{2}$ , And $X_{3}$ , Let

Multiple Choice

Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary.
-For mutually exclusive events $X_{1}, X_{2}$ , and $X_{3}$ , let $P\left(X_{1}\right) =.32, P\left(X_{2}\right) =.40$ , and $P\left(X_{3}\right) =.28$ . Also, $\mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{1}\right) =.40, \mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{2}\right) =.30$ and $\mathrm{P}\left(\mathrm{Y} \mid \mathrm{X}_{3}\right) =.60$ . Find $\mathrm{P}\left(\mathrm{X}_{3} \mid \mathrm{Y}\right)$ .

A) .40
B) .27
C) .31
D) .29