To solve this problem we will use the following formula to compute the theoretical probability that an event occurs:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]e) From the given table we get that there are 12 male students in Green club.
Since there are 100 students in total, we get that the theoretical probability of choosing a male student that is in Green club is:
[tex]\frac{12}{100}=\frac{3}{25}.[/tex]f) To answer this question we will use the following formula:
[tex]P(A\text{ given B)=}\frac{P(A\text{ and B)}}{P(B)}\text{.}[/tex]From the given table we get that there are 22 female students in Huskies with Heart, and there are a total of 58 female students, therefore:
[tex]\begin{gathered} P(\text{Female and Huskies)=}\frac{22}{100}=\frac{11}{50}, \\ P(\text{Female)}=\frac{58}{100}=\frac{29}{50}. \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} P(\text{Huskies given Female)=}\frac{P(Female\text{ and Huskies)}}{P(Female)} \\ =\frac{\frac{11}{50}}{\frac{29}{50}}=\frac{11}{29}. \end{gathered}[/tex]Answer:
e)
[tex]\frac{3}{25}\text{.}[/tex]f)
[tex]\frac{11}{29}\text{.}[/tex]