Question

The dart board is formed of concetric circles with radius 3 cm, 2 cm and 1 cm as shown in the figure below. What will be the probability of dart hitting the area A?

• A. 53 %
• B. 48 %
• C. 60 %
• D. 55.6 %

Answer 1

The correct option is D 55.6 %

Here the event is hitting in region A.

The total area of the circular region with radius 3 cm- $\pi r^2$ = 3.14 $\times$ 3 $\times$ 3 = 28.26 $c{m}^2$

Area of circular region A (i.e. ring A) = $\pi (3{)}^2$ - $\pi (2{)}^2$

Probability of dart hitting dart board in region A is =

P (A) = $\frac{AreaofcircularregionA}{TotalArea}$

= $\frac{\pi (3{)}^2-\pi (2{)}^2}{\pi (3{)}^2}$

= $\frac{9\pi -4\pi }{9\pi }$ = $\frac{5\pi }{9\pi }$

= $\frac{5}{9}$ = 0.556 = 55.6 %