What is Probability Calculator?
This probability calculator combines the probabilities of two independent events. Enter P(A) and P(B) as decimals from 0 through 1, and it returns P(A and B) and P(A or B). Both formulas explicitly depend on independence.
The tool does not infer whether events are independent, calculate conditional probability, accept percentages directly, count outcomes, or model mutually exclusive events as a separate case. You must determine that the independence assumption is appropriate.
Why Use This Tool?
Independent-event formulas are common but easy to confuse. AND multiplies probabilities, while inclusive OR adds them and subtracts the overlap to avoid double counting.
Displaying both results together helps compare the chance that both events occur with the chance that at least one occurs.
- Calculate an independent intersection.
- Calculate an independent inclusive union.
- Use decimal probabilities with six-decimal output.
How Does This Tool Work?
Enter each probability between 0 and 1. The calculator multiplies them for AND. For OR, it adds the probabilities and subtracts that product because the overlap is included in both individual values.
Results are rounded to six decimal places. Inputs outside the closed interval [0, 1] produce no result.
Understanding Your Results
P(A and B) is the probability that both independent events occur. P(A or B) is inclusive: A, B, or both may occur. Multiply a decimal output by 100 to interpret it as a percentage.
For valid independent events, AND cannot exceed either individual probability, while OR cannot be less than either and cannot exceed 1. These checks can help identify an input or assumption error.
Why Tracking This Matters
Probability arithmetic is only as valid as its assumptions. Events are independent when knowing one occurred does not change the probability of the other. Drawing without replacement, repeated behavior by the same subject, and shared causes often violate independence.
The calculator returns deterministic arithmetic, not evidence that a probability estimate is accurate. Sampling quality, model uncertainty, and event definitions remain outside the tool.
Benefits of Using Probability Calculator
- Independent AND and inclusive OR
- Strict 0-to-1 input validation
- Six-decimal result rounding
- Visible overlap subtraction
- No hidden probability model
- Browser-local calculation
How Is the Result Calculated?
For independent events, the intersection equals the product. The general union identity is P(A) + P(B) − P(A∩B); substituting the independent product produces the implemented OR formula.
P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A) × P(B)
- P(A)
- Probability of event A as a decimal from 0 to 1.
- P(B)
- Probability of event B as a decimal from 0 to 1.
- P(A or B)
- Inclusive probability that at least one event occurs.
- Both formulas assume independence in this implementation.
- No conditional probabilities are accepted.
- The calculator does not validate event definitions or estimated inputs.
Tips for Better Results
- Convert percentages to decimals before entry.
- Confirm independence rather than assuming it.
- Remember that OR is inclusive.
- Use conditional probability for dependent events.
- State the source and uncertainty of estimated probabilities.
Conclusion
Use this calculator only when two probabilities are expressed as decimals and the events can reasonably be treated as independent. The AND and inclusive-OR arithmetic is exact to the displayed rounding, but the assumptions and source probabilities determine whether the result is meaningful.