Worked example: Probability Calculator
Independent. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- P(A)
- 0.4
- P(B)
- 0.3
- Relationship
- Independent
| Calculated quantity | Example result |
|---|---|
| P(A and B) | 0.12 |
| P(A or B) | 0.58 |
| P(neither) | 0.42 |
| P(not A) | 0.6 |
Understanding data summaries and statistical uncertainty
Check the data before the summary
A mean summarizes total magnitude per observation, while a median locates the middle of an ordered data set. A few extreme values can affect them differently. Standard deviation describes spread in the original units; variance uses squared units. A frequency chart helps show distribution shape that one summary cannot capture.
Keep sample and population formulas distinct. A sample-variance calculation typically uses n−1 in its denominator. Repeated observations and units must be handled consistently, and a list of numbers does not by itself establish independent random sampling.
Choose the assumptions before reading the result
Confidence intervals, sample sizes and p-values depend on a specified model, confidence or tail convention, and data assumptions. A narrow calculated interval is not evidence that the assumptions were met. A p-value is not the probability that a hypothesis is true.
Use the page’s formula and worked example to check whether the statistic, sample size and degrees of freedom match the intended analysis. Do not substitute a population standard deviation for a sample value, or a one-sided test for a two-sided one, without changing the model.
Formula and calculation method
Independent intersection=P(A)P(B). Mutually exclusive intersection=0, requiring P(A)+P(B)≤1. Union=P(A)+P(B)−intersection.
Reference Sources
Frequently asked questions
How does this calculator work?
Independent intersection=P(A)P(B). Mutually exclusive intersection=0, requiring P(A)+P(B)≤1. Union=P(A)+P(B)−intersection.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.