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A genuine probability problem at Foxtrot

Posted on December 24, 2017 by admin

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*}

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