A genuine probability problem at Foxtrot | Rambling Nerd with a Plan

Genuine probability problem at Foxtrot

$\begin{align*} P(T\geq6) & = \sum_{n=6}^{10} {10 \choose n} p^n q^{10-n}\\ & = \sum_{n=6}^{10} {10 \choose n} \left ( \frac{1}{2} \right ) ^n \left ( \frac{1}{2} \right ) ^{10-n} \\ & = \sum_{n=6}^{10} {10 \choose n} \left ( \frac{1}{2} \right ) ^{10} \\ & = \frac{1}{1024} \sum_{n=6}^{10} {10 \choose n} \\ & = \frac{1}{1024} \left [ {10 \choose 6} + {10 \choose 7} + {10 \choose 8} + {10 \choose 9} + {10 \choose 10}\right ] \\ & = \frac{1}{1024} \left [ 210 + 120 + 45 + 10 +1\right ] \\ & = \frac{386}{1024}\\ & = 0.377 \end{align*}$