Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Simple probability assumes every outcome is equally likely, an assumption that holds for a fair coin or a fair die and breaks immediately for anything weighted or biased. Apply the same formula to a loaded die or a real-world event with unequal chances and the arithmetic still runs, but the answer it produces no longer describes the actual situation.
Before you rely on it
What to check
Confirm the equal-likelihood assumption actually fits your scenario before trusting the result. A weighted or biased situation needs different inputs, not this formula.
The common error
Where people go wrong with simple probability calculator
Applying equal-outcome probability to a real-world event that isn't actually equally likely. The math runs fine either way; only one of the two answers describes reality.
Sensitivity evidence
How favorable outcomes changes the probability
| Favorable outcomes | Probability | Odds against (to 1) |
|---|---|---|
| 2 | 3.8% | 25.00× |
| 3 | 5.8% | 16.33× |
| 4worked example | 7.7% | 12.00× |
| 5 | 9.6% | 9.40× |
| 6 | 11.5% | 7.67× |
Every input, tested
Which input moves the probability most
| Input | Tested from | To | Probability at each end | Swing |
|---|---|---|---|---|
| Favorable outcomes | 3 | 5 | 5.8% to 9.6% | 3.8% (50%) |
| Total outcomes | 47 | 57 | 8.5% to 7.0% | 1.5% (19%) |
Two variables at once
Probability by favorable outcomes and total outcomes
| Favorable outcomes \ Total outcomes | 42 | 52 | 62 |
|---|---|---|---|
| 2 | 4.8% | 3.8% | 3.2% |
| 3 | 7.1% | 5.8% | 4.8% |
| 4 | 9.5% | 7.7% | 6.5% |
| 5 | 11.9% | 9.6% | 8.1% |
| 6 | 14.3% | 11.5% | 9.7% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Favorable outcomes | 4 |
| Total outcomes | 52 |
| Probability | 7.7% |
| Odds against (to 1) | 12.00× |
Where the inputs come from
Enter the number of favorable outcomes and the total number of equally likely outcomes. For a deck of cards, four aces out of 52 cards gives 4 over 52. Make sure the outcomes are equally likely, or the ratio does not represent probability, and that you count each outcome once. The tool returns the probability as a percentage and the odds against the event.
When the result stops applying
The simple ratio only applies when outcomes are equally likely. Real events, such as weather or sports, are estimated from data, not counted. Combining events needs rules: probabilities of independent events multiply, and mutually exclusive events add. People often misjudge small probabilities and streaks.
What to compare it with
Count outcomes on the permutation and combination calculator, model repeated trials on the binomial probability page, and judge bets on the expected value calculator. The Bayes theorem and normal probability calculators handle updated and continuous cases.
People also ask
Frequently asked questions
How do I calculate probability?
Divide the number of favorable outcomes by the total number of equally likely outcomes and express the result as a percentage or decimal.
What is the difference between odds and probability?
Probability is favorable over total, while odds compare favorable to unfavorable, so a 1 in 4 probability is 1 to 3 in favor.
Does a coin become more likely to land heads after several tails?
No. Each flip is independent, so the chance stays 50% no matter what happened before, and believing otherwise is called the gambler's fallacy.