Use Bayes's Rule to Find the Indicated Probability A Student Is Selected at Random from the College

Multiple Choice

Use Bayes's rule to find the indicated probability.
-Among students at one college are 3936 women and 3197 men. The following table provides relative-frequency distributions for subject major for males and females at the college. $$\begin{array} { l c c } \text { Major } & \begin{array} { l } \text { Relative frequency } \\\text { for women }\end{array} & \begin{array} { c } \text { Relative frequency } \\\text { for men }\end{array} \\\hline \text { Humanities } & 0.207 & 0.157 \\\text { Science } & 0.299 & 0.354 \\\text { Social Science } & 0.171 & 0.375 \\\text { Other } & 0.323 & 0.114\end{array}$$ A student is selected at random from the college. Determine the probability that the student Selected is female given that he or she is a Humanities major.

A) 0.114
B) 0.619
C) 0.207
D) 0.637