Chapter 10.4, Problem 10E

To determine

Tocalculate:

The probability of student interview won an award for English or Mathematics.

Answer to Problem 10E

The probability of student interview won an award for English or Mathematics is $0.69$ .

Explanation of Solution

Given information:

Total students $=162$

Mathematics award winners $=48$

English award winners $=78$

Studnetsthose receive both awards mathematics and english $=14$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Calculation:

Assume that event $A$ denote students who won awards for mathematics and event $B$ denote students who won awards for English.

With the help of given information $14$ students are common to both $A$ and $B$ . Then probability of $A$ or $B$ is given as follows:

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\\ P\left(AorB\right)=\frac{48}{162}+\frac{78}{162}-\frac{14}{162}\\ =\frac{112}{162}\\ =0.69\end{array}$

Hence, the answer is $0.69$ .

So, the probability of student interview won an award for English or Mathematicsis $0.69$ .