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].
