Independent Events Calculator
Calculate the chance that all independent events occur, or that at least one occurs.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Probabilities | Enter probabilities from 0 to 1, separated by commas or line breaks. |
Understanding your result
These outputs describe the probability model and event definitions you entered. A probability is a number from 0 to 1; a probability density is not itself the probability of one exact continuous value.
Common mistakes
- Entering 25 instead of 0.25 for a probability, or assuming events are independent when the model requires that assumption.
- Confusing an exact-count probability with a cumulative probability, or replacement with sampling without replacement.
Check your calculation
- Check a zero/certain-event boundary and the stated support of the distribution against the worked example.
Calculation checks, sources and review limits
What is the chance of all independent events, or at least one of them, happening?
Calculate the chance that all independent events occur, or that at least one occurs.
Common uses
- Calculate the chance that all independent events occur, or that at least one occurs.
How it works
joint=product(p_i); atLeastOne=1-product(1-p_i) Lists accept commas, semicolons, spaces or line breaks as separators; use a dot for decimals. At most 10,000 observations are supported. Calculations use floating-point arithmetic; displayed numeric results have up to 12 significant digits.
Worked example
Enter Probabilities: 0.5, 0.2. The result is All: 0.1; At least one: 0.6.
FAQ
What is the chance of all independent events, or at least one of them, happening?
joint=product(p_i); atLeastOne=1-product(1-p_i) Lists accept commas, semicolons, spaces or line breaks as separators; use a dot for decimals. At most 10,000 observations are supported. Calculations use floating-point arithmetic; displayed numeric results have up to 12 significant digits.
What assumptions and limits apply?
Independence must be an explicit input assertion; correlated events require joint probabilities.