In a group of 26 students, 4 study both Art and Biology.
5 study Biology but not Art.
5 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
To find the probability that a student studies Art and Biology, we need to use conditional probability.
First, let's calculate the number of students who study Art only. We know that 5 students study Biology but not Art, so the number of students who study Art only would be 26 - 4 - 5 - 5 = 12.
Now, we can determine the probability that a randomly selected student studies Art and Biology using the formula for conditional probability:
P(Art and Biology) = P(Art and Biology) / P(Art)
P(Art and Biology) = (4 / 26) / (12 / 26)
Simplifying this expression, we get:
P(Art and Biology) = 4 / 12
Therefore, the probability that a randomly selected student studies Art and Biology is 1/3 or approximately 0.3333.