Question

Please solve this question

Answer 1

Hello,

$\boxed{P(X = k) =( {}^{n} _{k}) \times p {}^{k} \times (1 - p) {}^{n - k} }$

$P(X= k) = ( {}^{12} _{6}) \times 0.51 {}^{6} \times (1 - 0.51) {}^{12 - 6}$

We have :

$( {}^{n} _{k}) = \frac{n!}{k!(n - k)!}$

$( {}^{12} _{6}) = \frac{12!}{6!(12 - 6)!} = \frac{12!}{6!6!} = \frac{12 \times 11 \times 10 \times ... \times 1}{2(6 \times 5 \times 4 \times... \times 1) } = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 }{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 924$

$P(X = k) = 924 \times 0.51 {}^{6} \times 0.49 {}^{6} = 0.2250$