# Probability using percentages of percentages

(A) 55% of the students at a certain college are females.

(B) 7% of the students in this college are majoring in computer science.

(C) 4% of the students are women majoring in computer science.

If a student is selected at random, find the conditional probability that

(a) the student is female given that the student is majoring in computer science;

(b) this student is majoring in computer science given that the student is a female.

• Hint: think fractions, not percentage. I find it easier to manipulate concepts. – Martigan Nov 5 '14 at 15:40

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$
So for (a), let $A$ be the event that the student is female and $B$ be the event that the student is a CS major. Therefore, the conditional probability of female given cs major is $\frac{0.04}{0.07}=\frac{4}{7} \approx 57\%$.
For (b), reverse the events, so the conditional probability for cs major given female is $\frac{0.04}{0.55} \approx 7\%$.