Moment generating function, probability problem

Question

Given: $M_x(t) = \frac{1}{6} + \frac{1}{3} \exp(t) + \frac{1}{6} \exp(2t) + \frac{1}{3} \exp(3t)$.

What will be $P(X>2)$?

I couldn’t identify this moment generating function.

I guess if I could identify the mgf this will become easier.

Answer 1

As @StubbornAtom notes, you can read the probability distribution off viz.$$P(X=0)=\tfrac16,\,P(X=1)=\tfrac13,\,P(X=2)=\tfrac16,\,\color{blue}{P(X=3)=\tfrac13}.$$