If the random variable X has the following probability distribution:

then P(X ≤ 0) is equal to: 

$\frac{6}{13}$

In the given problem we have 

We know that the sum of total probability will always equal to one

so, k +2k + 3k + k/2 = 1

⇒ k = 1/3

Now P(X ≤ 0) = P(0) + P(-1)

                     = 2k + k

                     = 3k 

               Since k = 1/13

Hence P(X ≤ 0) = 3/13