Probability spaces

A circular target of unit radius is divided into four annular zones with outer radii 1/4, 1 /2, 3/4, and I, respectively. Suppose 10 shots are fired independently and at random into the target.

(a) Compute the probability that at most three shots land in the zone bounded by the circles of radius 1 /2 and radius 1.

(b) If 5 shots land inside the disk of radius 1 /2, find the probability that at least one is in the disk of radius 1 /4.

My answers:(a) [math] \displaystyle\sum_{k=0}^{3}\binom{10}{k}(\frac34)^k (\frac14)^{10-k}[/math] 

(b)[math] \frac{\displaystyle\sum_{k=1}^{5}\binom{5}{k}(\frac{1}{16})^k(\frac{3}{16})^{5-k}}{\binom{10}{5}(\frac14)^5(\frac34)^5}=1.275e-2[/math]

My answer to (a) is correct.

Author's answer for (b) is [math] 1- (\frac34)^5[/math] 

Whose answer is correct? My answer for (b) or author's answer for (b)?

Edited September 27, 20223 yr by Dhamnekar Win,odd
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