# Solution to simple student probability problem

1) At a certain university, 57% of students are female, 7% are enrolled in the Computer Science course and 6% are female and are studying Computer Science.

a) Calculate the probability that a student chosen at random at the university is a female, given that she studies Computer Science.

b) Calculate the probability that a student chosen at random at the University is enrolled at the Computer Science course, given that the student is a female.

I've used the Bayes Theorem here but couldn't get the right answer

• Can you show work? – drum Oct 12 '16 at 0:10
• This is what I've done (and it's wrong) A: Computer Science course B: female gender P(B|A) = [P(A|B)xP(B)]/P(A) P(B|A) = (0.06x0.57)/0.07 P(B|A) = 0.488 – statsucks Oct 12 '16 at 0:15

## 1 Answer

Cant really comment, but I think I dont understand the given statistics here. There is a university with 57% female students, 6% of the female students study computer science and 7% of all students study computer science?

In that case:

A: Calculate the probability that a random Computer Science student is a female. Then you have to calculate the female computer science portion of the university: 0.57 * 0.06 = 0.0342 (3.42%). Then you divide that by the 0.07: 0.0342 / 0.07 = ~0.48857 (48.9%) I guess...

B: Calculate the probability that a random female student is studying computer science. Isnt this just that 6%?

• You understood it right, but the answers are a. 0.857 b. 0.105 I'm not quite sure if that helps you to discover where we did it wrong. – statsucks Oct 12 '16 at 0:22
• a. sounds like 6% / 7%. – Wietlol Oct 12 '16 at 0:40