Question

The probability that a randomly selected student is on the honor roll is 0.24. The probability that a randomly selected student is on the honor roll and takes an art class is 0.18.

What is the probability that a randomly selected student takes an art class, given that the student is on the honor roll?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the probability that a randomly selected student takes an art class given that the student is on the honor roll, we can use the formula for conditional probability:

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

Where:
P(A|B) is the probability of event A given event B has occurred
P(A and B) is the probability of both events A and B happening
P(B) is the probability of event B happening

In this case, event A is the student taking an art class and event B is the student being on the honor roll.

Since we are given that the probability of a student being on the honor roll and taking an art class is 0.18, P(A and B) = 0.18

We are also given that the probability of a student being on the honor roll is 0.24, P(B) = 0.24

Therefore, the probability that a randomly selected student takes an art class given that the student is on the honor roll is:

P(A|B) = 0.18 / 0.24 = 0.75

So, the probability that a randomly selected student takes an art class, given that the student is on the honor roll is 0.75.