Probability Calculator

Probability shows up in dice games, card games, weather forecasts, and a huge chunk of introductory statistics classes, but the actual arithmetic gets confusing fast once a question involves two events instead of one — should you add the probabilities or multiply them, and does it matter if the events can happen together? This calculator handles both the basic case (favorable outcomes over total outcomes) and the two-event case (AND / OR combinations of independent events).

It's aimed at exactly the situations where people get tripped up: a single dice roll or card draw is usually intuitive, but combining two separate probabilities correctly is where a wrong intuition (adding when you should multiply, or the reverse) most often creeps in.

A single event's probability is favorable outcomes divided by total possible outcomes, expressed as a percentage — the chance of rolling a 4 on a standard die is 1 favorable outcome out of 6 total, or about 16.7%.

For two independent events (where one happening doesn't affect the other's chances), P(A and B) = P(A) × P(B) — both have to happen, so you multiply. P(A or B) = P(A) + P(B) − P(A)×P(B) — either one happening is enough, so you add them, then subtract the overlap where both happen, since that overlap would otherwise get counted twice.

'Independent' is the key assumption behind these formulas — it means the outcome of one event has zero effect on the probability of the other. Two separate dice rolls are independent; drawing two cards from a deck without replacing the first one is not, since removing a card changes the odds for the second draw.