Chapter 11.4, Problem 21PPSE

Solution

To identify :The percent of those who pass the first test also pass the second test. A math teacher gives her class two tests, 60% of the class passes both tests and 80% of the class pass the first test.

• What conditional probability are you looking for

• How can a tree diagram help you solve this problem

The required percentage of student pass first and also second test is $75\%$

Given information:

Math teacher gives her class students 2 tests. 60% of the class passes both tests and 80% of the class passes first test.

Explanation:

Consider the given information.

Determinethe pass percentages of students first test and also second test.

Probability of pass percentage of first and second test

  $\begin{array}{l}P\left(F\cap S\right)=60\%\\ P\left(F\right)=80\%\\ P\left(F/S\right)=\frac{P\left(F\cap S\right)}{P\left(F\right)}\\ =\frac{60\%}{80\%}\\ =75\%\end{array}$

The tree diagram for this problem

  

Therefore the required percentage of student pass first and also second test is $75\%$