Question

A dart is thrown at a circular dartboard such that it will land randomly over the area of the dartboard. What is the probability that it lands closer to the center than to the edge?

• A. 25%
• B. 30%
• C. 40%
• D. 20%

Answer 1

The correct option is A 25%

The set of outcomes are all of the points on the dartboard, which make up an area of $\pi$r², where r is the radius of the circle. The points that are closer to the center than to the edge are those that lie within the circle of radius $\frac{r}{2}$​ around the center, so the area of the "success" outcomes is $\pi$($\frac{r}{2}$)²=$\frac{\pi r²}{4}$.


P(closer to center than edge) =
$\frac{Areaofdesiredoutcomes}{Areaoftotaloutcomes}$= $\frac{\pi r²/4}{\pi r²}$= $\frac{1}{4}$= 25%