Question

Can you please help me out

Answer 1

In order to solve this question, we need to find the area of the yellow ring and the total area. The area of the yellow ring is equal to the area of the outer ring minus the area of the red circle, that is

$\begin{gathered} A_{\text{yellow}}=\pi4^2-\pi1^2 \\ A_{\text{yellow}}=16\pi-\pi \\ A_{\text{yellow}}=15\pi \\ A_{\text{yellow}}=47.124 \end{gathered}$

and the total area is the area of the entire square, that is

$\begin{gathered} A_{\text{total}}=10^2 \\ A_{\text{total}}=100 \end{gathered}$

Then, the probability that the dart is within the yellow outer ring is given by

$\begin{gathered} P(\text{inside yellow ring)=}\frac{A_{yellow}}{A_{total}} \\ P(\text{inside yellow ring)=}\frac{47.124_{}}{100} \end{gathered}$

then by rounding the numetaror to the nearest whole number , the answer is

$P(\text{inside yellow ring)=}0.47$