Probability Calculator

Simple probability: calculating likelihood from outcomes

Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%). A probability of 0 means the event is impossible; a probability of 1 means it is certain. Most real-world events fall somewhere in between. The basic formula for simple probability is: probability = favourable outcomes / total possible outcomes. This applies whenever all outcomes are equally likely, which is assumed in this calculator.

A classic example is rolling a fair six-sided die. There are 6 equally likely outcomes. The probability of rolling a 4 is 1/6, which equals approximately 0.1667 as a decimal and 16.67% as a percentage. The probability of rolling an even number (2, 4, or 6) is 3/6 = 1/2 = 0.5 = 50%. This calculator works through exactly that arithmetic for whatever numbers you provide.

The result shows the probability as a fraction (favourable / total), as a decimal to six decimal places, and as a percentage rounded to two decimal places. It also shows odds in favour (favourable : unfavourable) and odds against (unfavourable : favourable). Odds and probability are related but different: a probability of 1/4 equals odds in favour of 1:3, meaning one favourable outcome for every three unfavourable ones.

When you enter a number of trials, the calculator also shows the expected number of successes (probability times number of trials) and the probability of getting at least one success in that many trials. The "at least one" probability uses the complementary rule: 1 - (probability of failure)^trials. This is useful for scenarios like rolling a die multiple times and asking whether you will roll a 6 at least once.

Probability versus odds: what is the difference

Probability and odds both describe likelihood but in different ways. Probability is the fraction of outcomes that are favourable out of all outcomes. Odds compare favourable outcomes directly to unfavourable outcomes. If you have a 25% probability of winning, your odds in favour are 1:3 (one win for every three losses). Betting contexts typically use odds rather than probability, which is why understanding both representations is useful.

Odds against is the ratio most commonly quoted in betting: if the odds against winning are 3:1, you need to bet 1 unit to win 3 units (plus your stake back). Probability and odds always carry the same information but express it differently, and converting between them is straightforward with the formulas this calculator applies.

When does this probability model apply

This calculator uses the classical definition of probability, which assumes all outcomes are equally likely. This works for fair dice, fair coins, drawing cards from a well-shuffled standard deck, lotteries with uniform random draws, and similar idealized scenarios. It does not directly apply to situations where outcomes have different likelihoods, such as biased dice or real-world events where historical frequencies must be used instead of theoretical counts. For equally likely events, this tool provides exact results. For weighted probabilities or conditional probability, a more advanced probability tool would be needed.