Question

Oliver Queen is able to hit the bull's-eye (center of the target) 87% of the time. If he shoots 29 arrows, what is the probability that he hits the bull
eye exactly 13 times?

Answer 1

The probability that he hits the bull's-eye in one shot is given by p = 0.87

Then, the probability that the hits the bull's-eye m times in n shots is given by:

$P(m|n)=\frac{n!}{m!(n-m)!}p^m(1-p)^{n-m}$

For n = 29 and m = 13 we have:

$\begin{gathered} P(13|29)=\frac{29!}{13!16!}0.87^{13}\cdot0,13^{16} \\ P(13|29)=4.0\cdot10^{-8} \end{gathered}$