Chapter 0, Problem 22PO

To determine

To find: The probability that the student has passed the test given that he has passed the quiz.

Answer to Problem 22PO

The probability is 0.857.

Explanation of Solution

Given:

  $\begin{array}{l}P\left(\text{Passed the quiz}\right)=56\%=0.56\\ P\left(\text{Passed the quiz and Test}\right)=48\%=0.48\end{array}$

Calculation:

The probability that the student has passed the test given that he has passed the quiz is calculated as:

  $\begin{array}{c}P\left(\text{Passed the Test | Quiz}\right)=\frac{P\left(\text{Passed the Test and Quiz}\right)}{P\left(\text{Passed the quiz}\right)}\\ =\frac{0.48}{0.56}\\ =0.857\end{array}$

Thus, the required probability is 0.857.