Probability Calculator
Last updated: November 4, 2026
Combine two entered event probabilities under an explicit independence assumption.
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Quick summary: Combine two entered event probabilities under an explicit independence assumption.
Read the complete guide
Updated reference sections in this guide are in English.
Using this calculator
Enter the probabilities of events A and B as percentages between 0 and 100. This tool models independent events: knowing that one occurred must not change the chance of the other. The calculator does not infer independence from the two probabilities. Check that assumption against the experiment before interpreting the combined results.
Calculation method
P(both) = pq
P(at least one) = p + q − pq
P(neither) = (1 − p)(1 − q)
P(exactly one) = p(1 − q) + q(1 − p)
The “at least one” result is an inclusive union: it includes outcomes where both events occur. “Exactly one” excludes that overlap. Complements and combined results are returned as percentages again.
Worked examples
Two independent chances
With A = 25% and B = 40%, both occur with probability 10%. At least one is 25% + 40% − 10% = 55%. Neither is 75% × 60% = 45%, and exactly one is 45%.
An impossible event
If A = 0%, both events have probability zero, while at least one has the same probability as B.
Check this scenario in the calculator:
- Probability of event A (%)
- 25
- Probability of event B (%)
- 40
Understanding the result
The probabilities of neither, exactly one and both sum to 100%. Independent does not mean mutually exclusive: two nonzero independent events can happen together. Two mutually exclusive events with nonzero probabilities cannot be independent under this model.
Boundaries and assumptions
Percentages may include decimals but cannot fall below zero or above 100. Dependent events need additional information, such as an intersection or a conditional probability, which this form does not ask for. It does not derive chances from sample data, estimate uncertainty or decide whether a real-world outcome is likely.
Questions and reference
What if the events are dependent?
Do not use the combined-event values from this model. Obtain the relevant conditional or joint probability first.
Does “or” exclude both?
The “at least one” row includes both. The separate “exactly one” row excludes both.
Reference: OpenStax: independent and mutually exclusive events