How to use the Probability Calculator
Enter the probability of event A, the probability of event B and, if you like, a number of repeated trials. You get the chance of both, either, and at least one success.
Worked example
If A and B each have a 50% chance and do not affect each other, both happening is 0.5 × 0.5 = 25%, and at least one happening is 0.5 + 0.5 − 0.25 = 75%. Rolling at least one six in four rolls is 1 − (5/6) to the power 4, about 51.8%, which is a classic bet that wins slightly more often than it loses.
The independence assumption
These formulas assume one event does not change the chances of the other, like two coin flips or two dice. Drawing two cards without putting the first back is different, because the deck changes. For dependent events, multiply by the conditional probability instead of the plain one.
The formula
P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B)
Examples
- P(A) = 0.5, P(B) = 0.25, 3 trials
P(A and B): 0.125 P(A or B): 0.625 P(neither): 0.375 P(exactly one of A, B): 0.5
- P(A) = 0.2, P(B) = 0.1, 5 trials
P(A and B): 0.02 P(A or B): 0.28 P(neither): 0.72 P(exactly one of A, B): 0.26
Limitations and assumptions
Assumes the events are independent.
Frequently asked questions
How do I find the probability of two independent events both happening?
Multiply them: P(A and B) = P(A) × P(B).
How do I find either of two events?
P(A or B) = P(A) + P(B) − P(A and B).
How do I find at least one success in n trials?
1 − (1 − p)^n.
Are the events assumed independent?
Yes. If one event affects the other, conditional probability is needed.