Do you understand that $P[\text{respond}]=0.7$ ?
At least 3 never respond is the same situation as at most 1 responds.
So we have a binomial distribution to evaluate at $k=0,1$
$P[\text{at least 3 don't respond}] = P[\text{0 or 1 respond}] = (1-0.7)^4 + \dbinom{4}{1}(0.7)^1 (1-0.7)^3 = (0.3)^4 + 4 (0.3)^3(0.7)$
This is choice A.