If I were designing college curricula, an entry course of probability and statistics might be the only one I’d make mandatory.  Want to major in history or English?  That’s fine, but I don’t want you to check out of here with no understanding of how the most important underlying forces of nature work.

As the young fellow here points out, the topic can be broached much earlier in students’ math careers (though not before they’re proficient in adding and multiplying fractions and decimals).