# Probability of hitting the dart board in the second ring.

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 !!!

• What is the right answer? Jul 5 at 8:51
• The confusions seems to be about the definition of what second ring means. Is the right answer $1/9$? Jul 5 at 8:51
• @RishiSonthalia : Updated the question with the answer that has been given. Jul 5 at 9:09
• Dunno. Maybe it was meant to ask "third ring" (or the smallest is not counted as a ring because it is a disk). After all $16=5^2-3^2$. Jul 5 at 9:13

$$\frac{\pi \cdot (5^2 - 3^2)}{\pi \cdot 9^2} = \boxed{\frac{16}{81}}$$