The probability that X can take the values $x_i$ has the following form:

$P\left(X=x_i\right)=\left\{\begin{array}{lll} 0.2 & \text { if } ~~~x_i=0 \\ k x_i & \text { if } ~~~x_i=1 \text { or } 2 \\ k\left(5-x_i\right) & \text { if } ~~~x_i=3 \\ 0 & ~~~~~~\text { otherwise } \end{array}\right.$

The value of P(X = 2) is:

$\frac{8}{25}$

The correct answer is Option (4) → $\frac{8}{25}$