Probability Calculator — Build a Valid 2 × 2 Table
Enter P(A) and P(B), choose their relationship, and see every outcome add up to 100%.
Relationship used
| B | Not B | Total | |
|---|---|---|---|
| A | |||
| Not A | |||
| Total | 100% |
P(A | B)
P(B | A)
Choose what you actually know
Independent multiplies P(A) and P(B). Mutually exclusive sets the intersection to zero. Known intersection uses the P(A and B) you enter and checks whether it is possible for the two marginal probabilities.
The four cells are the audit
The table separates both events, A only, B only, and neither. Every cell must be nonnegative and the four cells must total 100%. That catches impossible intersections before they are used in union or conditional-probability formulas.
Bounded scope
This page handles two finite events expressed as percentages. It does not calculate normal distributions, infer a relationship from data, or predict gambling, medical, financial, or machine-learning outcomes.
Frequently asked questions
How do you calculate the probability of A or B?
Use P(A or B) = P(A) + P(B) - P(A and B). Subtracting the intersection prevents outcomes that belong to both events from being counted twice.
Are mutually exclusive events independent?
Usually no. Mutually exclusive events cannot occur together, so their intersection is zero. Independent events can occur together and use P(A and B) = P(A) × P(B). Only zero-probability edge cases can satisfy both descriptions.
What values can P(A and B) have?
The intersection must be at least max(0, P(A) + P(B) - 1) and at most min(P(A), P(B)). This calculator shows that legal range and rejects combinations that would create a negative cell.
What is conditional probability?
P(A given B) = P(A and B) / P(B) when P(B) is greater than zero. If the conditioning event has probability zero, the displayed conditional probability is undefined.
Does this calculator predict gambling outcomes?
No. It only checks arithmetic for two stated event probabilities. It does not estimate real-world odds, infer dependence, or provide betting advice.