Question

In a circular dartboard of radius 25cm, there are 5 concentric circles. the radius of each inner concentric circle is 5 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.

• A. $\frac{1}{5}$
• B. $\frac{1}{25}$
• C. $\frac{1}{\pi }$
• D. 1

Answer 1

The correct option is B

$\frac{1}{25}$

Difference in radius between 2 circles = 5cm

Let, radius of small circle be x.
$\Rightarrow$ x + 5 + 5 + 5 + 5 = 25 (from the diagram)
$\Rightarrow$x = 5cm

Probability that the dart hits anywhere in the small circle = $\frac{ar\left(innermostcircle\right)}{ar\left(outermostcircle\right)}$

$=\frac{\pi {.5}^2}{\pi {25}^2}$

$=\frac{1}{25}$