At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c c }
& \mathrm { C } & \overline { \mathrm { C } } & \
\text { Women } & .45 & .25 & .70 \
\text { Men } & .05 & .25 & .30 \
& .50 & 50 & 1.00
\end{array}$

Question

At a college,70 percent of the students are women,and 50 percent of the students receive a grade of C.25 percent of the students are neither female nor C students.Use this contingency table.
$\begin{array} { l c c c } 
& \mathrm { C } & \overline { \mathrm { C } } & \
\text { Women } & .45 & .25 & .70 \
\text { Men } & .05 & .25 & .30 \
& .50 & 50 & 1.00
\end{array}$

Quizplus · Accepted Answer

To find the probability that a student is a man and receives a C, we can use the formula: P(M ∩ C) = P(C | M) * P(M). We know that P(M) = 0.30, and we need to find P(C | M). Since we know that 50% of the students receive a C, and 25% are neither female nor C students, we can find that 75% of the students are either female C students or male C students. Since 70% of the students are female, we can subtract 70% from 75% to find that 5% of the students are male C students. Therefore, P(C | M) = 0.05/0.30 = 0.17. So, P(M ∩ C) = 0.17 * 0.30 = 0.05. Thus, the answer is D.

At a College,70 Percent of the Students Are Women,and 50