> I'm puzzled by the fact that the probability term was RAISED to the number of hours, rather then multiplied by it? so the chance isn't linear with the amount

> I'm puzzled by the fact that the probability term was RAISED to the number of hours, rather then multiplied by it? so the chance isn't linear with the amount of time ? Yes it is not linear. Imagine you are repeatedly throwing a dice. The probability that you get a "6" at some point is absolutely not linear with the number of throws: P(not a single "6" in N throws) = (4/5)^N so P(at least one "6" in N throws) = 1 - (4/5)^N Edit: Also, raw probabilities are constrained to the interval [0, 1]. So they are rarely linear in a parameter, because, then, they would easily escape the [0, 1] interval. Imagine that we had P(covid) = some_constant * some_parameter. There would be values of the parameter such that P(covid) > 1, which does not make sense.