Question

Assume that the male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly 8 boys in 10 births.

Answer 1

We can model using the Binomial Distribution:
$$
P(X=8)=\binom{10}{8}0.5^80.5^2\\
=\cfrac{10\times9}{2}\times\cfrac{1}{2^{10}}\\
=\cfrac{45}{2^{11}}
$$
http://en.wikipedia.org/wiki/Binomial_distribution#Probability_mass_function

Hope this helps.