Question

1. college courses at a large university, the probability that a student takes calculus and is on the deans list is 0.042. the probability that a student is on the deans list is 0.21. find the probability that the student is taking calculus, given that he or she is on the deans list.

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that a student takes calculus and \(B\) be the event that a student is on the dean's list. We are given \(P(A\cap B) = 0.042\) and \(P(B)=0.21\).

Step2: Substitute the values into the formula

Substitute \(P(A\cap B) = 0.042\) and \(P(B)=0.21\) into the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). So \(P(A|B)=\frac{0.042}{0.21}\).

Step3: Calculate the result

\(\frac{0.042}{0.21}=0.2\)

Answer:

\(0.2\)