If the random variable X has the following probability distribution:

then P(X ≤ 0) is equal to: 

$\frac{6}{13}$

Given

$X : -1,\,0,\,1,\,2$

$P(X=x) : k,\,2k,\,3k,\,\frac{k}{2}$

Total probability $=1$

$k+2k+3k+\frac{k}{2}=1$

$6k+\frac{k}{2}=1$

$\frac{13k}{2}=1$

$k=\frac{2}{13}$

Now

$P(X\le0)=P(X=-1)+P(X=0)$

$=k+2k=3k$

$=3\left(\frac{2}{13}\right)=\frac{6}{13}$

$P(X\le0)=\frac{6}{13}$.