Consider the random variable \(X\) representing the time until a light bulb fails to work after being successfully turned on. Notice that the bulb could fail in a relatively short time (near 0 let’s say) or could continue to last for almost eternity (or as long as you might want to measure). However, time is measured on a continuum and therefore for this random variable \(X\) you would have \(R\) equal to the interval from 0 to infinity, i.e. \(R = (0,\infty)\) which is not a countable set.