Question

An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{24}{25}$
• D. $\frac{25}{100}$

Answer 1

The correct option is C $\frac{24}{25}$


$\text{Radius of the outer circle}=25inches.$
$\text{Area of the outer circle}=\pi \times {25}^2=625\pi sq.in$

$\text{Radius of the bullseye}=5inches.$
$\text{Area of the bullseye}=\pi \times 5^2=25\pi sq.in$

$\text{Area of the target}without\text{bullseye}=625\pi -25\pi =600\pi sq.in$

$\text{Probability of missing the bullseye but still}\text{hitting the target}=\frac{\text{Area of the target}without\text{the bullseye}}{\text{Total area of the target}}=\frac{600\pi sq.in}{625\pi sq.in}=\frac{24}{25}$