Probability Calculator
Find the probability of two events happening together or separately. Enter P(A) and P(B) to get P(A and B), P(A or B), the complements, and the conditional probability.
- P(A and B)
- 0.1500
- P(A or B)
- 0.6500
- P(not A)
- 0.5000
- P(not B)
- 0.7000
- P(A | B)
- 0.5000
How to use this calculator
- Enter the probability of each event as a decimal between 0 and 1.
- Choose whether the events are independent or mutually exclusive.
- Read the combined and complementary probabilities.
The probability rules
For independent events, whether one happens does not change the other:
For mutually exclusive events, both cannot happen at once:
The complement of an event is P(not A) = 1 − P(A), and the conditional probability is P(A | B) = P(A ∩ B) / P(B).
Independent vs. mutually exclusive
Frequently asked questions
What is the difference between independent and mutually exclusive events?
Independent events do not affect each other and can both occur. Mutually exclusive events cannot occur at the same time, so their joint probability is zero. Two events with positive probability cannot be both independent and mutually exclusive.
How do I find P(A and B)?
For independent events, multiply the probabilities: P(A and B) = P(A) × P(B). For mutually exclusive events, P(A and B) = 0 because they cannot both happen.
What is conditional probability?
Conditional probability P(A | B) is the probability of A given that B has occurred. It equals P(A and B) divided by P(B).