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

Question

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

Quizplus · Accepted Answer

To find the probability that a randomly selected student is female given they are a Humanities major, we use Bayes's rule. First, calculate the total probability of being a Humanities major by multiplying the relative frequencies by the total number of women and men, then summing those products. Then, divide the probability of being a female Humanities major by this total probability. Calculation: $P(Female|Humanities) = \frac{0.207 \times 3936}{(0.207 \times 3936) + (0.157 \times 3197)} \approx 0.619$.

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