Question

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

• A. $\frac{r^2}{R^2}$
• B. $\frac{r}{R}$
• C. $\frac{R}{r}$
• D. 1

Answer 1

The correct option is A

$\frac{r^2}{R^2}$

Area of board = $\pi$ $R^2$
Area of bull's eye = $\pi$ $r^2$
Here, we shall use the concept of geometric probability as the number of outcomes are not finite.
$\text{The probability of hitting the bull's eye}$
$=\frac{\text{Area of the bull's eye}}{\text{Area of the board}}$=$\frac{\pi .r^2}{\pi .R^2}$ = $\frac{r^2}{R^2}$