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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 !!!

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  • $\begingroup$ What is the right answer? $\endgroup$ Jul 5 at 8:51
  • $\begingroup$ The confusions seems to be about the definition of what second ring means. Is the right answer $1/9$? $\endgroup$ Jul 5 at 8:51
  • $\begingroup$ @RishiSonthalia : Updated the question with the answer that has been given. $\endgroup$
    – Ganit
    Jul 5 at 9:09
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    $\begingroup$ 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 $16=5^2-3^2$. $\endgroup$
    – drhab
    Jul 5 at 9:13

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The confusion seems to be in the way ring is defined. The question should have made this more clear, in my opinion.

enter image description here

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

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

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