Answer
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:
$\begin{align}
& P\left( y \right)=\frac{54}{144} \\
& =\frac{3}{8}
\end{align}$
