Let $W$ be the time you wait for the traffic light at an intersection turn GREEN, if it is RED. Suppose that you find that the light at the intersection is GREEN with probability $p = \frac{1}{4}$ (Since there is no wait, so $W = 0$). With probability $p' = 3/4$ you find that the light is RED.
Let $W$ be exponential random variable with rate $\lambda = 1/5$ : Assume that there is no traffic jam at the intersection and you pass the light as soon as it's GREEN. Compute:
a) C.D.F
b) E(W)
\begin{align} \mathbb{E}(W) &= \left[\dfrac{1}{4} \times 0\right] + \left[ \dfrac{3}{4}\mathbb{E}(W|\lambda)\right] \\ & = \dfrac{3}{4} \times \lambda^{-1} \tag{mean of an exponential r.v. is $\lambda^{-1}$} \\ & = \dfrac{15}{4} \end{align}