Chapter 0.6, Problem 14E

To determine

To find: The probability that a student takes AP Calculus given that he or she is on the honor roll.

Answer to Problem 14E

The probability that a student takes AP Calculus given that he or she is on the honor roll is 0.152.

Explanation of Solution

Given information:

Suppose the probability that a student takes AP Calculus and is on the honor roll is 0.0035 and the probability that a student is on the honor roll is 0.23.

Calculation:

We have two events that need to be labeled with simple letters, we choose "A" and "B".

Let A be for AP Calculus and B for honor roll.

Probability taking AP Calculus and enrolled in Honors roll is $P\left(A\text{ and }B\right)=0.0035$ .

Probability that student is in honor rollis $P\left(B\right)=0.23$ .

From conditional probability rules, we can find probability that student is taking AP Calculus given that student is being enrolled in honor roll.

  $\begin{array}{c}P\left(A/B\right)=\frac{P\left(A\text{and}B\right)}{P\left(B\right)}\\ =\frac{0.0035}{0.23}\\ =0.0152\end{array}$

Thus, the probability that a student takes AP Calculus given that he or she is on the honor roll is 0.152.