Theoretical Probability

Pre-Algebra · Axiom Academy

LESSON Theoretical Probability When every outcome is equally likely, a probability is just one fraction: how many outcomes you want, over how many there are. Every theoretical probability is one fraction. The top counts the favorable outcomes — the ones that make the event happen. The bottom counts all the equally likely outcomes. A fair coin has two equally likely sides, and exactly one of them is heads. Each outcome must be equally likely The bar fills to that fraction of the whole 2. Counting the Favorable Outcomes Usually more than one outcome counts as a win. To find the probability of rolling an even number on a fair die, we count every face that is even — that's the favorable subset — and put it over all six faces. The animation shades the even faces and fills the bar to exactly that share of the row. A fair die has 6 equally likely faces: 1, 2, 3, 4, 5, 6. That's the denominator. The even faces are 2, 4, and 6 — three of them. That's the numerator. Three favorable over six total. Half the faces are even, so the bar fills halfway. reduces to — the same value, written more simply. What about rolling a number greater than 4 ? Now only 5 and 6 are favorable, so . The denominator never changed — only which faces we counted on top.

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