Question

At a large university, the probability that a student takes calculus and is on the dean's list is 0.027. The probability that a student is on the dean's list is 0.26. Find the probability that the student is taking calculus, given that he or she is on the dean's list. Please round the final answer to 2 or 3 decimal places. P(the student is taking calculus given that he or she is on the dean's list) =

Answer 1

The probability that a student is taking calculus given that they are on the dean's list is approximately 0.104.

Step-by-step explanation:

To find the probability that a student is taking calculus given that they are on the dean's list, we can use the concept of conditional probability. Let's denote the event of a student taking calculus as C and the event of a student being on the dean's list as D.

From the information given, we know that P(C ∩ D) = 0.027 (the probability that a student takes calculus and is on the dean's list) and P(D) = 0.26 (the probability that a student is on the dean's list).

The formula for conditional probability is P(C|D) = P(C ∩ D) / P(D). Plugging in the values we have, we get:

P(C|D) = 0.027 / 0.26 = 0.1038

Rounding the final answer to 3 decimal places, the probability that the student is taking calculus, given that he or she is on the dean's list, is approximately 0.104.