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Probability Calculator — Compute the Chance of an Event
The probability calculator computes the chance of an event using the classical method. Enter the number of favorable and total possible events and pick a mode (single event, complement or two independent). The tool returns the probability as a percentage, as a decimal fraction, and the chance that the event happens at least once in two trials.
How the calculator computes probability
p = favorable events / total events (clamped to range 0–1) Modes: Single = p Complement = 1 − p Two independent = p × p (both events occur) Results: Probability (%) = result × 100 Decimal fraction = result rounded to 4 places At least one (%) = (1 − (1 − p)²) × 100 for two trials
Example: a die roll, chance of a six
Die roll: 1 favorable event (a six) out of 6 total
p = 1/6 = 0.1667, i.e. 16.67%. The complement (not rolling a six) is 83.33%. For two coin flips (p = 1/2) the chance both land heads is 25%, and at least one is 75%.
Frequently asked questions
What is classical probability?
It is the ratio of favorable events to all equally likely events: P = favorable / total. For a die, the chance of a six is 1/6 ≈ 0.1667, i.e. about 16.67%. The condition is that all outcomes are equally likely.
How does the complement rule work?
The probability that an event does NOT occur is 1 minus the probability it occurs: P(not A) = 1 − P(A). For 1/6 that gives 1 − 0.1667 = 0.8333, i.e. 83.33%. The “complement” mode computes exactly this value.
How do I compute two independent events?
For independent events the chance both occur is the product: P(A and B) = P(A) × P(B). When both have probability p, the result is p². For p = 1/2 that is 0.5 × 0.5 = 0.25, i.e. 25%. The “two independent” mode computes this.
What does “at least one” mean?
It is the chance that, in two independent trials, the event happens at least once: 1 − (1 − p)². For p = 1/2 that gives 1 − 0.25 = 0.75, i.e. 75%. The calculator shows this value next to the main result.
How do probability and odds differ?
Probability is the ratio of favorable cases to all cases (1/6). Odds are the ratio of favorable to unfavorable cases (1:5). You convert odds with P = odds / (odds + 1). Odds of 1:5 equal a probability of 1/6 ≈ 16.67%.
What is the gambler’s fallacy?
It is the belief that past results affect the next draw in independent games. If a coin landed heads five times in a row, the chance of tails is still 50% — the coin does not remember past flips. Independent events do not even out in the short run.
Why is probability between 0 and 1?
Every probability is a number from 0 to 1 (0%–100%). A value of 0 means an impossible event, and 1 a certain one. The calculator clamps the result to this range, so entering more favorable than total gives 100%.
How do theoretical and empirical probability differ?
Theoretical probability comes from a model (1/6 for a die), while empirical probability is the ratio of observed successes to the number of trials. By the law of large numbers, the empirical value approaches the theoretical one as trials grow.
How do I compute the probability of a union of events?
For mutually exclusive events P(A or B) = P(A) + P(B). When they can occur together, use inclusion–exclusion: P(A or B) = P(A) + P(B) − P(A and B). This calculator handles a single event, its complement and two independent trials.
Is this calculator suitable for games and betting?
It shows mathematical probabilities assuming equally likely, independent outcomes. Real games and bets include the operator’s margin, so odds do not reflect pure probability. Treat the results as an educational tool.
Indicative result
Results are educational and assume equally likely, independent events. They are not gambling advice or a guarantee of any outcome. Real games of chance and betting involve the operator’s margin and other factors.
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