Probability Calculator

Probability turns uncertainty into a number between 0 and 1, and the way you combine events changes the math entirely. This calculator handles the four core cases: a single event, two events both happening, either event happening, and one event given another.

Students working through statistics problems use it to check answers; anyone reasoning about chance — dice, cards, risk — uses it to get the math right. It expresses each result as a decimal, a simplified fraction, and a percentage, and for single events it also gives the odds for and against, the format gamblers and bookmakers use.

For equally likely outcomes, probability is the count of favourable cases divided by the total. The tool reports that as a decimal, a percentage, and a simplified fraction, since different contexts conventionally use different forms.

It also converts to odds, which express the same information as a comparison rather than a proportion. Odds in favour are favourable cases against unfavourable ones — not against the total — which is the distinction that makes betting odds confusing at first. A probability of one in four is odds of one to three, not one to four.

Both fraction and odds are reduced by their greatest common divisor, so the output is in lowest terms.

The basic combination rules are worth knowing. For independent events both occurring, multiply their probabilities. For mutually exclusive events, either occurring, add them. Where events can overlap, adding alone double-counts the overlap and it must be subtracted back out. And the probability that something does not happen is one minus the probability that it does — often the easier route to an answer.

Two errors recur. The gambler's fallacy treats independent events as though they have memory: a coin that has landed heads five times is no more likely to land tails next, because the coin does not know. And the conjunction fallacy leads people to rate a detailed, plausible scenario as more likely than a broader one that contains it, when adding conditions can only ever reduce probability.

The equally-likely assumption underneath this calculation is also worth checking. It holds for fair dice, shuffled cards, and balanced coins, and fails for almost anything in the real world — weather, illness, sporting results — where probabilities must be estimated from data rather than counted from a sample space.