Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1120: 70


The probability that the target will land in the yellow region is $\frac{3}{8}$.

Work Step by Step

We have to find the probability that the dart hits the shaded region, by using the following formula: $\begin{align} & P\left( E \right)=\frac{\text{Area of the shaded region}}{\text{Total area of the sqaure}} \\ & =\frac{\text{area}\left( \text{shaded} \right)}{\text{area}\left( \text{total} \right)} \end{align}$ $\begin{align} & \text{Shaded area}=\text{area of square of 9 in}+\text{area of the square of 3 in}-\text{area of the square of 6 in} \\ & ={{\left( 9 \right)}^{2}}+{{\left( 3 \right)}^{2}}-{{\left( 6 \right)}^{2}} \\ & =81+9-36 \\ & =54 \end{align}$ $\begin{align} & \text{Total area of the figure}={{\left( 12 \right)}^{2}} \\ & =144 \end{align}$ So, the probability that the dart will land in the yellow region is as follows: $\begin{align} & P\left( y \right)=\frac{54}{144} \\ & =\frac{3}{8} \end{align}$
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