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 $p=1-q$ ....$\left(\text{iii}\right)$

Solving $\left(\text{i}\right)$ , $\left(\text{ii}\right)$and $\left(\text{iii}\right)$ we get,

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

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

$={}^{32}C_{1}p{q}^{31}+{}^{32}C_2{p}^2{q}^{30}$

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