Probability Calculator
0.50
0.30
Operation
Probability Result0.150000
FormulaP(A and B) = P(A) x P(B)
Probability describes how likely an event is, on a scale from 0 (impossible) to 1 (certain). This calculator combines the probabilities of two events using the standard rules for independent events: the chance both happen, the chance at least one happens, the complement of an event, and a conditional probability. Enter the probability of A and of B and choose the operation.
Formula
P(A and B) = P(A)·P(B); P(A or B) = P(A) + P(B) - P(A)·P(B); P(not A) = 1 - P(A)
- P(A)
- Probability of event A, between 0 and 1
- P(B)
- Probability of event B, between 0 and 1
How it works
- Enter the probability of event A and, where needed, the probability of event B as decimals between 0 and 1.
- Pick an operation. "AND" multiplies the two probabilities, "OR" adds them and subtracts the overlap, "NOT" returns one minus P(A), and "GIVEN" applies the conditional formula P(A and B) / P(B), which for independent inputs returns P(A).
Worked example
Two independent events have P(A) = 0.5 and P(B) = 0.4. Find both the AND and the OR probabilities.
- P(A and B) = 0.5 × 0.4 = 0.2.
- P(A or B) = 0.5 + 0.4 - (0.5 × 0.4) = 0.9 - 0.2 = 0.7.
There is a 0.2 chance both occur and a 0.7 chance at least one occurs.
Frequently asked questions
- Does the AND rule assume the events are independent?
- Yes. This calculator multiplies P(A) by P(B), which is correct only when the two events are independent. For events that influence each other you would need the actual joint probability instead.
- Why does the OR formula subtract a term?
- For the union of two events you add their probabilities, but that double-counts the overlap where both happen. Subtracting P(A)·P(B) removes that double-counted region so the total never exceeds 1.
- What does the GIVEN (conditional) option compute?
- It applies P(A given B) = P(A and B) / P(B) using P(A and B) = P(A)·P(B), so for the independent inputs used here it simplifies to P(A). If P(B) is 0 the conditional probability is undefined and the tool returns 0.