And vs Or Probability

Pre-Algebra · Axiom Academy

One survey, two questions, two very different answers — seen on a Venn diagram you can drive yourself. Two tiny words, two different answers We asked 12 students which they like: pizza, ice cream, or both. Now ask two questions that sound almost the same. How many like pizza AND ice cream? And how many like pizza OR ice cream? Swapping one word swaps the answer — and "OR" hides a trap that catches almost everyone. Watch the count build. The Pizza circle holds 8 students; the Ice Cream circle holds 8 . It's tempting to say "pizza OR ice cream" is 8+8=16 — but there are only 12 students! The 4 in the middle got counted twice. Watch them get subtracted back out. "OR" isn't just adding the two groups — you add them, then subtract the overlap once so nobody is counted twice. That correction is the whole story of AND vs OR. AND is the overlap; OR is everything Same 12 students. Flip between the two questions and watch which part of the diagram you're counting. AND keeps only the overlap — the students in both circles. OR keeps every student in either circle. One word, two regions, two probabilities. AND gives — restrictive, both must be true. OR gives here — inclusive, either one will do. AND is almost always the smaller of the two. Move the overlap and watch both answers shift

This is the written version of the interactive lesson above. See the full Pre-Algebra course.