# 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
Commented Oct 12, 2016 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 Commented Oct 12, 2016 at 0:15

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. Commented Oct 12, 2016 at 0:22
• a. sounds like 6% / 7%. Commented Oct 12, 2016 at 0:40