If the sum and the product of mean and variance of a binomial...

Let $p =$probability of success and $q =$probability of failure,

Now given,

Sum $np + npq = 24 . . . \left(\text{i}\right)$

Product $np \times npq = 128 . . . \left(\text{ii}\right)$

Also $p = 1 - q$ ....\left(\text{iii}\right)$</p><p>Solving \left(\text{i}\right)$ , \left(\text{ii}\right)$and \left(\text{iii}\right)$ we get,

$p = \dfrac{1}{2}, q = \dfrac{1}{2}, n = 32$

Now, $P\left(X = 1\right) + P\left(X = 2\right)$

$= C1 32 p{q}^{31} + C2 32 {p}^{2}{q}^{30}$

$= \dfrac{33}{{2}^{28}}$