Classical Probability

When every outcome is equally likely, probability is just bookkeeping: count the outcomes you want, divide by all the outcomes there are. Gerolamo Cardano wrote the first honest analysis of this in his Liber de Ludo Aleae around 1564 — a gambler's handbook so frank about cheating that it stayed unpublished until 1663 — and Laplace made it the formal definition in 1812. A single die has six faces, three of them even, so P(even) = 3/6 = 0.5. Enter probabilities here as decimals between 0 and 1, or switch the unit to % if you prefer 50 to 0.5.

The trap is the phrase "equally likely". Rolling two dice gives eleven possible totals, 2 through 12, but they are not equally likely: there are 36 equally likely face-pairs, and six of them total 7 while only one totals 12, so P(7) = 6/36 ≈ 0.167 against P(12) = 1/36 ≈ 0.028. Always count the underlying equal outcomes, never the labels people put on them. Run the formula backwards to size a sample space: if 13 of the cards in a deck are hearts and P = 0.25, then n = 13/0.25 = 52.