Answer:
[tex]P(F/S)=0.216[/tex]
Step-by-step 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:
[tex]\frac{646}{x}+\frac{229}{x}-0.06=1[/tex]
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:
[tex]P=\frac{229}{825.47} =0.2774[/tex]
Because there are 825.47 students and 229 are senior.
So, P(F/S) is equal to:
[tex]P(F/S)=\frac{0.06}{0.2774}=0.216[/tex]
