Question

Use the chart below to answer the following questions (100 students total):FemalesClubMalesHuskies with Heart2022Green Club2312158Book Cluba Find the probabilty that a randomly chosen student is in Green Club and Male:f.Find the probability that given a student is female, that she is in Huskies with Heart.

Answer 1

To solve this problem we will use the following formula to compute the theoretical probability that an event occurs:

`\frac{\text{favorable cases}}{total\text{ cases}}.`

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:

`(12)/(100)=(3)/(25).`

f) To answer this question we will use the following formula:

`P(A\text{ given B)=}\frac{P(A\text{ and B)}}{P(B)}\text{.}`

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:

`\begin{gathered} P(\text{Female and Huskies)=}(22)/(100)=(11)/(50), \\ P(\text{Female)}=(58)/(100)=(29)/(50). \end{gathered}`

Therefore:

`\begin{gathered} P(\text{Huskies given Female)=}\frac{P(Female\text{ and Huskies)}}{P(Female)} \\ =((11)/(50))/((29)/(50))=(11)/(29). \end{gathered}`

Answer:

e)

`(3)/(25)\text{.}`

f)

`(11)/(29)\text{.}`