In a group of 44 students, 3 study both Art and Biology.
4 study Biology but not Art.
10 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
whats the overall answer
To find the probability that a randomly selected student studies both Art and Biology, we need to use the concept of conditional probability. The conditional probability of an event A given that event B has occurred is denoted as P(A|B) and is calculated as the probability of A and B occurring together divided by the probability of B occurring.
In this case, we want to find P(Art and Biology | Art). Let's break down the information given:
- The total number of students is 44.
- Out of these 44 students, 3 study both Art and Biology.
- 4 students study Biology but not Art.
- 10 students study neither Art nor Biology.
Since we know that a randomly selected student studies Art, the total number of students who study Art is 44 minus the number of students who study neither subject (10 students), which is 34.
Using this information, let's calculate the probability.
P(Art and Biology | Art) = (Number of students studying Art and Biology) / (Number of students studying Art)
Number of students studying Art and Biology = 3
Number of students studying Art = 34
P(Art and Biology | Art) = 3 / 34 ≈ 0.0882
Therefore, the probability that a randomly selected student studies both Art and Biology, given that they study Art, is approximately 0.0882 (or 8.82%).
After making a Venn diagram , filling in all the given data and
finding that 27 take only Art, I realize that none of that was needed, since
you said,
3 study both Art and Biology, and there were 44 students, so
the Prob(Art and Biology) = 3/44