Probability Calculator
Calculate single- and multiple-event probabilities — A and B, A or B, the complement, and draws with or without replacement — from the chances of each event.
P(A and B)
0.25
25%
P(A or B)
0.75
75%
P(not A)
0.5
P(not B)
0.5
P(neither)
0.25
Independent AND: P(A)×P(B). OR: P(A)+P(B)−P(A and B). Complement: 1−P. At least once over n trials: 1−(1−P)ⁿ.
Frequently Asked Questions
How do I calculate the probability of two events both happening?
For independent events, multiply their probabilities: P(A and B) = P(A) × P(B). For example, the chance of two coin flips both landing heads is 0.5 × 0.5 = 0.25.
How do I calculate the probability of either event happening?
Use P(A or B) = P(A) + P(B) − P(A and B). Subtracting the overlap avoids double-counting outcomes that satisfy both events. For mutually exclusive events the overlap is zero, so it simplifies to P(A) + P(B).
What is the complement of a probability?
The complement is the chance an event does not happen: P(not A) = 1 − P(A). It is often the easiest route to 'at least one' problems — find the chance of none, then subtract from 1.
What is the difference between with and without replacement?
With replacement, the item is returned before the next draw, so probabilities stay the same and draws are independent. Without replacement, the pool shrinks each time, so later probabilities change and the draws are dependent.
How do I find the probability of an event over multiple trials?
For the chance an event happens on every one of n independent trials, raise its probability to the nth power: P^n. For the chance it happens at least once, use 1 − (1 − P)^n.