\(\mathbb P(X<6)=\mathbb P(X=0)+\mathbb P(X=1)+\cdots+\mathbb P(X=5)\)
\(X\) appears to have a binomial distribution, which means
\(\mathbb P(X=x)=\dbinom Nx p^x(1-p)^{N-x}\)
where \(\dbinom nk=\dfrac{n!}{k!(n-k)!}\). So, as an example, you could compute
\(\mathbb P(X=0)=\dbinom{20}00.3^0\times0.7^{20}=0.7^{20}\approx0.0007979\)
You should get
\(\mathbb P(X<6)=\displaystyle\sum_{x=0}^5\mathbb P(X=x)\approx0.4162\)
