Probability Calculator
Work out P(A and B), P(A or B), P(neither) and more for two independent events.
How to use the Probability Calculator
- Enter the probability of a – As a decimal (0.25) or a fraction (1/4).
- Enter the probability of b.
- Enter the number of repeated trials for a (optional).
- Press Calculate. The result updates automatically as you type.
About the Probability Calculator
Probability measures how likely an event is on a scale from 0 (impossible) to 1 (certain). When two events are independent, such as flipping a coin and rolling a die, you multiply to find the chance both happen and use the complement rule to find the chance that at least one happens without double counting the overlap.
The "at least once" result is often surprising. An event with a 50% chance per try almost certainly happens at least once in 5 tries (96.875%), and even a 1-in-100 chance happens at least once in 100 tries about 63% of the time. If your events affect each other, such as drawing two cards without replacement, these independent-event formulas do not apply; use conditional probability instead.
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 at least once in n trials) = 1 − (1 − P(A))ⁿ
These formulas assume A and B are independent, meaning one happening does not change the chance of the other.
Example calculation
Using the default values:
- Probability of A = 0.5
- Probability of B = 0.4
- Number of repeated trials for A (optional) = 5
the calculator returns:
- P(A and B): 0.2 (20%)
- P(A or B): 0.7 (70%)
- P(exactly one): 0.5 (50%)
- P(neither): 0.3 (30%)
- P(not A): 0.5 (50%)
- P(not B): 0.6 (60%)
- Odds of A: 1 : 1 in favor
- P(A at least once in n trials): 0.96875 (96.875%)
- P(A every time in n trials): 0.03125 (3.125%)
Frequently asked questions
How do I find the probability of two events both happening?
For independent events, multiply their probabilities. A 0.5 chance and a 0.4 chance together give 0.5 × 0.4 = 0.2, or 20%.
Why do I subtract P(A and B) when finding P(A or B)?
Adding P(A) and P(B) counts the outcomes where both happen twice, so you subtract that overlap once.
What is the difference between probability and odds?
Probability compares favorable outcomes to all outcomes; odds compare favorable to unfavorable. A probability of 0.2 is odds of 1 to 4.
Last updated: · Category: Math calculators