> Unless you are dealing with subjects that would actually use calculus, people in their day to day lives would do much better to understand probabilities, statistics and experiment design.

Probability theory is applied analysis. For example a measure density is a derivation of a measure with respect to another measure (Radon–Nikodym derivative). Or how do you often assign probabilities to measurable set: Lebesgue-Stieltjes integral.

So you better have a very good understanding of calculus before starting with probability and statistics.