The world is probabilistic. The world is driven by statistical - stochastic - processes. That does not mean the world is chaotic, uncontrolled, or even uncontrollable.
I drive my car on I-25 to Denver office when I'm in town. Out in the country side, the speed limit is 75MPH. No one of course is going 75. Here in Colorado, open road driving is 80 to 85. My car - a Fire Engine Red Honda SI - moves right along at 85. I stay in the lane, but the steering inputs are small random movements. At the lowest level the inputs are stochastic. A random, non deterministic behavior. But I stay in the lane.
When we think of a project's's cost and schedule, those are stochastic processes as well. They are random non-deterministic processes. By deterministic we mean "knowing the EXACT outcome. The underlying numbers are probabilistic, they are not deterministic. But that's doesn't mean they are chaotic. They are random wihtin the probability distribution driving their behaviour. The stochastic process driving their behaviour. This is lost many times in the conversation about "big anything up front." No credible project manager believes that the numbers - cost, schedule, and technical performance - are deteministic. To do so is basic nonsense. I know it happens, but that doesn't not make it nonsense.
So let's look at some definitions here.
Each task durations are defined as "most likley" but have probabilitic durations as well. The shape of the probability distribution curve may vary for each "class" work, risk level, and other drivers of variance. The actual schedule looks like this.