jmc

There are $2^{10}=1024$ possible outcomes of the 10 coin flips. The number of ways to get 8, 9, or 10 heads is $\left(\genfrac{}{}{0ex}{}{10}{8}\right)+\left(\genfrac{}{}{0ex}{}{10}{9}\right)+\left(\genfrac{}{}{0ex}{}{10}{10}\right)=45+10+1=56$. So the probability is $\frac{56}{1024}=\boxed{\frac{7}{128}}$.