The calculation, without hidden assumptions
The hard part of a probability question is often choosing the right relationship, not pressing calculate. This workspace keeps independent events, overlapping events, conditional probability and complements in one canonical owner, shows the substitution, and rejects impossible overlap combinations instead of returning a plausible-looking wrong answer.
How to use this calculator
Choose the probability relationship that matches the question.
Enter probabilities as decimals from 0 to 1; for dependent/general overlap modes, enter P(A ∩ B) explicitly.
Read the primary answer, companion probabilities and the deterministic formula substitution.
Where people use it
- •Probability and statistics homework
- •Risk and quality-control scenarios
- •Checking independent versus overlapping event calculations
Example: two independent events
If P(A)=0.5 and P(B)=0.4 and independence is justified, P(A and B)=0.20, P(A or B)=0.70 and P(neither)=0.30.
What the result does not assume
- •Do not assume independence merely because it makes the arithmetic easier. Use the general-overlap or conditional mode when events are dependent.
- •This owner handles core two-event relationships. Probability distributions and Bayes diagnostic models are materially different jobs and are not hidden inside this calculator.
Frequently asked questions
What is the difference between independent and mutually exclusive events?+
Independent events do not change each other’s probability. Mutually exclusive events cannot happen together; with positive probabilities they are not independent.
Why can an overlap value be invalid?+
For given P(A) and P(B), the intersection must stay between max(0, P(A)+P(B)-1) and min(P(A),P(B)). The calculator enforces those bounds.
What does P(A | B) mean?+
It is the probability of A after restricting attention to outcomes where B occurred, calculated as P(A and B) divided by P(B).
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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