Question

Find the probability that a dart hits the region X(inner circle) if the radius of the outer circle is $x$ times radius of the inner circle (x>2).

• A. $\frac{1}{x}$
• B. $\frac{1}{x^2}$
• C. $\frac{1}{x^3}$
• D. 1

Answer 1

The correct option is B

$\frac{1}{x^2}$

Let the radius of innermost circle = y

$\Rightarrow$radius of outermost circle = $yx$

Probability that a dart hits region X = $\frac{\text{Area (innermost circle)}}{\text{Area (outermost circle)}}=\frac{\pi .y^2}{\pi .y^2{x}^2}\Rightarrow \frac{1}{x^2}$