Probability Calculator
Combine two probabilities with and, or, not, or conditional rules. Toggle independence or type P(A and B) when events depend on each other.
Rated 4.7 out of 5 based on 388 reviews
How to combine event probabilities
- Choose and, or, not, or conditional from the operation list.
- Enter P(A). For not, that is the only probability you need. For the other modes, also enter P(B).
- For and or or, set Independent to Yes to use product rules, or No and type P(A and B) when the events share outcomes.
- For conditional, enter P(A and B) and P(B). Read the result rows. Errors for impossible combinations appear in the status line. Nothing is uploaded.
Two-event probability helpers
Intersection, union, complement, and conditional
| Operations | And, or, not, conditional |
|---|---|
| Independent and | P(A ∩ B) = P(A) × P(B) |
| Independent or | P(A ∪ B) = P(A) + P(B) − P(A)P(B) |
| Complement | P(not A) = 1 − P(A) |
| Conditional | P(A|B) = P(A ∩ B) / P(B) |
| Dependent path | Optional typed P(A and B) when independence is off |
What this probability page covers
This calculator is a small rule kit for two labeled events. And multiplies under independence or echoes a typed joint. Or uses the inclusion formula with either the product joint or a typed joint. Not flips a single probability. Conditional divides the joint by P(B). It is not a Venn diagram drawer and not a continuous density integrator.
How each operation runs
Independent and returns P(A) times P(B). Dependent and requires P(A and B) between 0 and min(P(A), P(B)) and also reports the implied conditionals. Independent or subtracts the product; dependent or subtracts the typed joint (blank joint counts as 0). Not returns 1 minus P(A). Conditional needs a finite joint and a nonzero P(B), with the joint no larger than P(B).
Independence, joints, and related entities
Core entities: event probability, independence, joint probability, complement, and conditional probability. Updating a prior with a supplied evidence rate is Bayes theorem. Exact success counts in n Bernoulli trials belong on binomial probability. Choosing k items from n without regard to order is combinations, which feeds many discrete probability word problems.
Use cases
Quick checks that 0.5 and 0.4 independent events give and = 0.2 and or = 0.7. Homework that states a joint instead of independence. Complement drills such as P(not A) from a typed P(A). Not a replacement for a full sample-space listing when outcomes are unequally likely in a way the book has not summarized into probabilities.
When to turn independence off
Leave independence on when the problem says the events do not affect each other. Turn it off when the text gives P(A and B) directly, or when overlap is nonzero and you must subtract that overlap in the union. Conditional mode always wants the joint typed; it does not multiply P(A) and P(B) for you.
Limits
Only two events. No three-way inclusion-exclusion. No continuous CDFs. Probabilities outside 0 to 1, empty required fields, or joints that break set inequalities fail in the status line. CZNull does not receive the numbers.