Question

If given a dart board of radius 50 cm. What is the probability that you hit the bull's eye of radius 5 cm?

• A. $\frac{1}{100}$
• B. $\frac{1}{10}$
• C. 1
• D. $\frac{1}{1000}$

Answer 1

The correct option is A

$\frac{1}{100}$

Area of board = $\pi$ $\times$ ${50}^2$ = 2500 $\pi$

Area of bull's eye = $\pi$ $\times$ $5^2$ = 25 $\pi$

Since we are dealing in areas, we will use the concept of Geometric Probability.

The probability of hitting the bull's eye= $\frac{\text{Area of required region}}{\text{Total area}}$ = $\frac{25\pi }{2500\pi }$ = = $\frac{1}{100}$