A boy is throwing stones at a target. The probability of hitting...

The probability of hitting the target 5 th time at the 10 th throw $=\mathrm{P}($ the probability of hitting the target 4 times in the first 9 throws) $\mathrm{P}($ the probability of hitting the target at the 10 th throw $)=\left[{ }^{9} \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{5}\right]\left(\frac{1}{2}\right)=\frac{9 !}{4 ! 5 !} \times\left(\frac{1}{2}\right)^{10}=\frac{63}{2^{9}}$