EX 4.3 waiting time of haircut

Let $X$ represent the amount of time a randomly selected customer spends waiting for a haircut before his/her haircut commences. Your first thought might be that $X$ is a continuous random variable, since a measurement is required to determine its value. However, there are customers lucky enough to have no wait whatsoever before climbing into the barber’s chair. So it must be the case that $P\left(X=0\right)>0.$ Conditional on no chairs being empty, though, the waiting time will be continuous since $X$ could then assume any value between some minimum possible time $A$ and a maximum possible time $B$ . This random variable is neither purely discrete nor purely continuous but instead is a mixture of the two types.