Question

The student council at Richmond High School

is made up of 646 female students 229
seniors, and 6% female seniors.
If a student is selected at random, what is the
probability, as a decimal to the nearest
hundredth, that the student is female given that
the student is a senior?

Answer 1

`P(F/S)=0.216`

Explanation:

Let's call F the event that the student is female and S the event that the student is senior.

So, we need to find the probability P(F/S) that a student is female given that the student is a senior. P(F/S) is calculated as:

P(F/S) = P(F∩S)/P(S)

Then, the probability P(F∩S) that a student is female and senior is equal to 0.06

On the other hand, we can calculate the total number of students x using the following equation as:

`(646)/(x)+(229)/(x)-0.06=1`

Where 646/x is the percentage of female students, 229/x is the percentage of senior students and 0.06 is the percentage of female seniors.

Then, solving for x we get that the number of students is 825.4719

Additionally, the probability P(S) that a student is a senior is equal to:

`P=(229)/(825.47) =0.2774`

Because there are 825.47 students and 229 are senior.

So, P(F/S) is equal to:

`P(F/S)=(0.06)/(0.2774)=0.216`