Question

In a group of 28 students, 12 study both Art and Biology.

12 study Biology but not Art.
4 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?

Answer 1

100%

Explanation:

Use conditional probability:

P(B | A) = P(B and A) / P(A)

P(B | A) = (12/28) / P(A)

We need to find the probability that a student studies art.

P(A or B) = P(A) + P(B) − P(A and B)

24/28 = P(A) + (12+12)/28 − 12/28

P(A) = 12/28

P(B | A) = (12/28) / (12/28)

P(B | A) = 1

What this means is that all of the students who study art also study biology.