The Moment Generating Function (MGF) of random variable $X$ is given by $M_{X}(t)=(\frac{e^{-t}+e^{t}}{2})^{3}, t\ge0$ then $P(|X|>1)$ is
Show Hint
When an MGF is a power of a sum of exponentials like $(\sum p_i e^{t x_i})^n$, the variable is a sum of $n$ i.i.d. variables. Recognizing the Bernoulli form $\frac{e^t + e^{-t}}{2}$ (Rademacher distribution) makes these discrete probability problems much faster to solve.