Probability Calculator
Drawing an ace from a standard deck is 4 favorable outcomes in 52, a 7.69% probability with odds of 1 to 12. This probability calculator turns favorable and total outcomes into a probability, its complement, and the odds notation. It also answers the question that trips everyone up: the chance of the event happening at least once across repeated tries.
Quick answer
Probability = favorable outcomes / total outcomes, when all outcomes are equally likely.
Probability
7.6923%
Complement
92.3077%
Odds for
1 to 12
At least once
7.6923%
What this tells you
- •Probability = favorable outcomes / total outcomes, when all outcomes are equally likely.
- •The complement, 1 - P, is the chance the event does not happen.
- •Odds compare favorable to unfavorable directly: 4 aces against 48 other cards is 1 to 12.
- •Across n independent tries, P(at least once) = 1 - (1 - p)^n, which grows faster than most people expect.
How to Use
- 1Enter the favorable outcomes, the ways the event can happen.
- 2Enter the total possible outcomes.
- 3Set the number of trials to 1 for a single attempt, or higher for repeated tries.
- 4Read the probability, complement, odds, and the at-least-once chance.
How It Works
Formula
P = favorable / total, P(at least once in n) = 1 - (1 - P)^nThe basic ratio counts equally likely outcomes: 4 aces over 52 cards gives 0.0769. For repeated independent tries, it is easier to track the event never happening, (1 - p)^n, and subtract from 1. A 7.69% chance per draw (with replacement) becomes a 55% chance of at least one ace across 10 draws.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Drawing an ace
4 aces among 52 cards. The complement, no ace, is 92.31%.
Rolling a six at least once in 4 rolls
1 - (5/6)^4. Four rolls make a six more likely than not, a classic dice result.
A 1% drop over 100 attempts
Not the 100% intuition suggests. (0.99)^100 still leaves a 36.6% chance of nothing.
At Least Once Over Repeated Trials
How a 10% single-trial chance compounds across attempts.
| Trials | P(at least once) |
|---|---|
| 1 | 10% |
| 5 | 41% |
| 10 | 65.1% |
| 20 | 87.8% |
| 50 | 99.5% |
Common mistakes
- Multiplying the single-trial chance by the trials. Ten tries at 10% is a 65% chance of at least one success, not 100%.
- Confusing probability with odds. A 7.69% probability is odds of 1 to 12, not 1 to 13, since odds compare against failures only.
- Applying the formula to unequal outcomes. Favorable over total only works when every outcome is equally likely, a loaded die breaks it.
- Treating dependent events as independent. Drawing cards without replacement changes the totals after every draw.