Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). For equally likely outcomes, it’s simply the number of favorable outcomes over the total possible outcomes.
Worked examples
Rolling a 4 on a fair six-sided die: 1 favorable outcome out of 6, so P = 1 ÷ 6 ≈ 0.167, or about 17%. Drawing a heart from a 52-card deck: 13 hearts ÷ 52 cards = 0.25, or 25%.
Combining events
- Independent events (AND) — multiply. Two coin flips both heads: 1/2 × 1/2 = 1/4.
- Mutually exclusive events (OR) — add. Rolling a 1 or a 2: 1/6 + 1/6 = 1/3.
- Complement (NOT) — subtract from 1. Not rolling a 4: 1 − 1/6 = 5/6.
Probability can be written as a fraction, a decimal, or a percentage — they’re the same value (1/4 = 0.25 = 25%).
Frequently asked questions
What’s the basic probability formula? Favorable outcomes divided by total possible outcomes.
Chance of two things both happening? Multiply their probabilities if they’re independent.
Can probability be more than 1? No — it ranges from 0 to 1 (0% to 100%).
A useful sanity check: the probabilities of all possible outcomes must add up to 1. If your event probabilities sum to more or less than 100%, you’ve either double-counted or missed an outcome — a quick way to catch mistakes before they compound.