It doesn’t, especially at the introductory level. Sure, at a certain point, it would be needed, but that would be for someone wanting to become a statistician, not the general population.
Beyond introductory level both probability and statistics have a lot of "counterintuitive" pre-probability and statistics results, that also explain a lot of the misconceptions the public faces in not understanding the notions.
Probability and statistics are topics that our democracies would be better of if people understood them: then they would understand perhaps topics like polling, and we wouldn't perhaps have misuse of the topics in Court like Sally Clark's case: https://en.wikipedia.org/wiki/Sally_Clark
[But I guess we would have to drop lotteries as a taxation system also. [/s]]