There is a shooting event organised by the SBT youth Club to select
the best candidate who will qualify to participate in Eklavya
championship. The shooting board is designed by using $4$ concentric
circles of radii $2$ inch, $3$ inch, $5$ inch and $9$ inch. What is
the probability that the participant will shoot only in the second
ring to qualify for Eklavya championship?
Total area = $81\pi $
Area of the second ring = $5\pi$
So shouldn't the probability will be = $\frac{5}{81}$
But this is not the right answer. The correct answer that has been given is $\frac{16}{81}$ and I am not able to get that how can this be the answer? What am I doing wrong? Please help !!!
Thanks in advance !!!
Best Answer
The confusion seems to be in the way ring is defined. The question should have made this more clear, in my opinion.
The red circle in the centre of the above dart board does not represent a ring. Only the green and blue regions are rings. Therefore, the second ring corresponds to the blue region.
Hence, the answer is
$$\frac{\pi \cdot (5^2 - 3^2)}{\pi \cdot 9^2} = \boxed{\frac{16}{81}}$$