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analysis of this in his Liber de Ludo Aleae around 1564 (a gambler's handbook so frank about cheating that it stayed unpublished until 1663) and Laplace made it the formal definition in 1812.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.