A discrete random variable X has the following probability distribution :

The value of $P(X≤2)$ is :

$\frac{9}{25}$

The correct answer is Option (3) → $\frac{9}{25}$

The sum of all probabilities must be equal to 1:

$P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=1$

$⇒4c^2+3c^2+2c^2+c^2+c+2c=1$

$c=\frac{-3±7}{20}⇒c=\frac{4}{20}=0.2$  (Probabilities must be positive)

$∴P(X≤2)=4c^2+3c^2+2c^2$

$=4(0.2)^2+3(0.2)^2+2(0.2)^2$

$=0.16+0.12+0.08$

$=0.36$