Final answer:
To find the probability that a randomly selected student studies both Art and Biology, we can use conditional probability. Given the provided information, the probability that a student studies Art and Biology, given that they study Art, is 11/15 or approximately 0.7333.
Step-by-step explanation:
To find the probability that a randomly selected student studies both Art and Biology, we need to use the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability of a student studying Art and Biology, given that the student studies Art.
Let's define some variables:
- P(A) = Probability of studying Art
- P(B) = Probability of studying Biology
- P(A and B) = Probability of studying both Art and Biology
We are given that P(A and B) = 11 (11 students study both Art and Biology), P(A') = 4 (4 students study neither subject), and P(B|A') = 15 (15 students study Biology but not Art).
Using these values, we can calculate the probability of a student studying both Art and Biology given that the student studies Art:
P(B|A) = P(A and B) / P(A)
P(B|A) = 11 / (34 - 4 - 15)
P(B|A) = 11 / 15
Therefore, the probability that a randomly selected student studies Art and Biology, given that the student studies Art, is 11/15 or approximately 0.7333.