A dart is randomly thrown at a circular board on which two concentric rings of radii $R$ and $2R$ having the same width (width much less than $R$) are marked. The probability of the dart hitting the smaller ring is:
(a). Twice the probability that it hits the larger ring.
(b). Half of the probability that it hits the larger ring.
(c). Four times the probability that it hits the larger ring.
(d). One-fourth the probability that it hits the larger ring.
My attempt:
Since the area of the larger ring is $4$ times the area of the smaller ring, the probability of the dart hitting the smaller ring is one-fourth the probability that it hits the larger ring. Therefore, option (d) is correct.
The answer key says that the correct answer is the option (b). Please help.
P.S. This is a question of CSIR-NET exam held in Dec, $2019$.
Best Answer
It's because the width is the same. The area is proportional to radius times width so if you double everything then it's a factor of 4, but if you only double the radius then it's a factor of 2.