One hundred college seniors attending a career fair at a university were categorized according to gender and primary career motivation. The table below shows the results. If one of these students is selected at random, find the probability that the student selected is female, given that their primary motivation is a sense of giving to society.

\begin{tabular}{|c|c|c|c|c|}
\hline & \multicolumn{3}{|c|}{ Primary Career Motivation } & \multirow[b]{2}{*}{ Total } \\
\hline & Money & \begin{tabular}{l}
Allowed to be \\
Creative
\end{tabular} & \begin{tabular}{l}
Sense of \\
Giving to \\
Society
\end{tabular} & \\
\hline Male & 14 & 7 & 11 & 32 \\
\hline Female & 3 & 32 & 33 & 68 \\
\hline Total & 17 & 39 & 44 & 100 \\
\hline
\end{tabular}

The probability that the student selected is female, given that the primary motivation is a sense of giving to society, is [tex]$\square$[/tex]
(Simplify your answer. Type an integer or a fraction.)



Answer :

To find the probability that the student selected is female, given that their primary motivation is a sense of giving to society, we need to follow these steps:

1. Identify the total number of students whose primary motivation is a sense of giving to society.
- From the table, the total number of students with this motivation is 44.

2. Identify the number of female students whose primary motivation is a sense of giving to society.
- From the table, there are 33 female students with this motivation.

3. Calculate the probability using the conditional probability formula.
- The conditional probability formula for this scenario is:
[tex]\[ P(\text{Female} \mid \text{Sense of Giving to Society}) = \frac{\text{Number of Females with Sense of Giving to Society}}{\text{Total Number of Students with Sense of Giving to Society}} \][/tex]

4. Substitute the numbers into the formula:
[tex]\[ P(\text{Female} \mid \text{Sense of Giving to Society}) = \frac{33}{44} \][/tex]

5. Simplify the fraction:
[tex]\[ \frac{33}{44} = \frac{3}{4} = 0.75 \][/tex]

So, the probability that the student selected is female, given that their primary motivation is a sense of giving to society, is [tex]\(\frac{3}{4}\)[/tex].