A random variable X has the following probability distribution

Then $P (X < 3)$ is

0.4

The correct answer is Option (4) → 0.4

Given:

$P(X=0) = 0.1$, $P(X=1) = k$, $P(X=2) = 0.2$, $P(X=3) = 2k$, $P(X=4) = 0.3$, $P(X=5) = k$

Total probability must sum to 1:

$0.1 + k + 0.2 + 2k + 0.3 + k = 1$

$0.6 + 4k = 1$

$4k = 0.4 \Rightarrow k = 0.1$

Now, compute $P(X < 3) = P(X=0) + P(X=1) + P(X=2)$

$= 0.1 + k + 0.2 = 0.1 + 0.1 + 0.2 = {0.4}$