Where will the coin drop?

If the radius $1$ cm coin, once dropped randomly, must lie entirely within the larger circle, then its center must lie within a circle of radius $40 - 1 = 39$ cm.

For the radius $1$ cm coin to also lie entirely within the smaller circle, which itself lies entirely within the larger circle, its center must lie within a circle of radius $20 - 1 = 19$ cm.

Thus the probability that the radius $1$ cm coin lies entirely within the smaller circle, given that it lies entirely within the larger circle, is

$\dfrac{\pi*19^{2}}{\pi*39^{2}} = 0.2373$

to 4 decimal places. This does not match any of the options, but is closest to $22.56$ %.

@Nik Olson It's a bit unclear when you say that the coin is dropped randomly "inside the larger circle". If it must lie entirely within the larger circle then you get my answer, but if only the coin's center must lie within the larger circle then you get your's and Baby Googa's answer. I believe that my interpretation of "inside the larger circle" is more intuitive, so since we are essentially looking at where the center can lie I think the option of $23.73$ % should be added and considered as the correct option. As mentioned above, I chose the $22.56$ % option because it was the closest value to my calculation.

Area of smaller circle is 1/4 of larger, so probability of landing in smaller is 1/4. But the coin must be entirely in the smaller circle (not just its centre) so it's 'a bit less than 1/4, ie a bit less than 25%.

The area of the possible outcomes is 1600\pi.

The area of the successful outcomes is 361\pi.

361\pi/1600\pi = 361/1600 = 22.56