The probability distribution of a random variable X is given by

If $k > 0$, then $P(0 < X ≤ 2)$ is equal to

$\frac{5}{6}$

The correct answer is Option (2) → $\frac{5}{6}$

Given the probability distribution:

X:      0         1         2
P(X):   k         2k        3k

The total probability must be 1:

$k + 2k + 3k = 6k = 1 \Rightarrow k = \frac{1}{6}$

Now, compute $P(0 < X \leq 2) = P(1) + P(2)$

$= 2k + 3k = 5k = 5 \cdot \frac{1}{6} = \frac{5}{6}$