Question

In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding the outer concentric circle. What is the probability that the dart hits the smallest circle?

Answer 1

Given,

Difference in radius between 2 circles = 4cm

Let, radius of small circle be x.
$\Rightarrow$ x + 4 + 4 + 4 + 4 = 20 (from the diagram)
$\Rightarrow$x = 4cm

Probability of an event, $P\left(E\right)=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

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

$=\frac{\pi \times 4^2}{\pi \times {20}^2}$

$=\frac{1}{25}$

Therefore, the probability that the dart hits anywhere in the small circle is $\frac{1}{25}$.