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Probability Calculator

Find the probability and odds of an event.

How it is calculated

For equally likely outcomes, the probability of an event is P = favorable outcomes / total outcomes. The tool shows it as a percentage (P × 100) and as odds written 1 : (total − favorable) / favorable, meaning one favourable outcome for that many unfavourable ones. The favorable count cannot be negative or larger than the total, and the total must be above zero. With zero favorable outcomes the percentage is 0% and the odds show a dash. The formula only works when every outcome is equally likely; it does not handle weighted outcomes or combinations of several events.

Worked example

Probability of drawing an ace from a standard 52-card deck: 4 favorable cards out of 52. P = 4 / 52 = 0.0769, which is 7.69%. Odds are shown as 1 : (52 − 4) / 4 = 1 : 12.00, meaning one ace for every 12 other cards.

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Common mistakes

  • Dividing favorable by unfavorable outcomes, which gives the odds ratio rather than the probability.
  • Reading "1 : 12" in this tool (1 favourable outcome to 12 unfavourable ones) as "one in 12" trials; that would be 1 : 11.
  • Assuming outcomes are equally likely when they are not, such as a loaded die or a weighted draw.
  • Using this for repeated events and adding probabilities; several draws need multiplication or other rules.

About this calculator

This calculator applies the classical probability formula, P(event) = favorable outcomes / total outcomes, and also converts the result into odds format (e.g., 1 : 3, which is 3-to-1 against), since both notations are used in different contexts.

Statistics students use it for coursework on dice, cards, and coin-flip problems; anyone evaluating a game of chance or a raffle uses it to see their real chances; and it underlies basic risk assessment questions like the probability of drawing a specific card from a deck or winning a lottery. The calculator keeps the result expressed as a clean fraction, decimal, and percentage side by side, since different fields (gambling odds vs. statistics vs. everyday conversation) tend to prefer different formats.

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Comments (1)

  • Editorial team

    The odds line is favourable to unfavourable outcomes: for an ace in a 52-card deck there are 4 aces and 48 other cards, so it shows 1 : 12, while the probability line gives 7.69 percent, about one chance in 13. The tool covers a single draw only. For at least one success in several independent tries, use 1 − (1 − p)^n: one six in six rolls of a die is about 66.5 percent, not 100. What game are you checking?

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