We have,
1st circle – with radius 3
2nd circle – with radius 7
3rd circle – with radius 9
So, their areas would be
Area of 1st circle = π(3)2 = 9π
Area of 2nd circle = π(7)2 = 49π
Area of 3rd circle = π(9)2 = 81π
Area of shaded region = Area of 2nd circle – Area of 1st circle
= 49π − 9π
= 40π
Probability that it will land on the shaded region
Therefore, the probability that the dart will land on the shaded region is
40
81
40
.
