Question

Assume that a dart will hit the dart board and each point on the dart board is equally likely to be hit in all the three concentric circles where radii of concentric circles are $3$ cm, $2$ cm and $1$ cm as shown in the figure below.
Find the probability of a dart hitting the board in the region $A$. (The outer ring)

Answer 1

In given radius of area $C$ is $1,B$ is $2$ and $A$ is $3$.

Then total area of circular region with radius $3$ cm $=$ $\pi (3{)}^2=9\pi$

The area of circular region with radius $2$ cm $=$ $\pi (2{)}^2=4\pi$

Then heating area of region $A=$ $9\pi -4\pi =5\pi$

Then probability of a dart hitting board region $A=$ $\frac{\text{area of region A}}{\text{total area of circular disc}}=\frac{5\pi }{9\pi }=0.55$

Then probability of a dart hitting board region $A=55\%$.