It depends on the choice being made. If you're considering one of several routes on the way to work, you don't care about arrival time, you only care about prob

It depends on the choice being made. If you're considering one of several routes on the way to work, you don't care about arrival time, you only care about probability of arriving before a certain time. In any case, the calculation isn't the point. My point is that in any non-trivial choice, you are necessarily making such a calculation, even if only approximately.