Question

Please solve this question

Answer 1

Hello,

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

`P(X= k) = ( {}^(12) _(6)) * 0.51 {}^(6) * (1 - 0.51) {}^(12 - 6)`

We have :

`( {}^(n) _(k)) = (n!)/(k!(n - k)!)`

`( {}^(12) _(6)) = (12!)/(6!(12 - 6)!) = (12!)/(6!6!) = (12 * 11 * 10 * ... * 1)/(2(6 * 5 * 4 *... * 1) ) = (12 * 11 * 10 * 9 * 8 * 7 )/(6 * 5 * 4 * 3 * 2 * 1) = 924`

`P(X = k) = 924 * 0.51 {}^(6) * 0.49 {}^(6) = 0.2250`