Probability Calculator
Work out the odds of a single event, then combine two independent events to see the chance of both, either, or neither landing.
Single event
Two independent events (enter each as 0–1)
How it works
For a single event, probability is favorable outcomes divided by total outcomes. Rolling a 4 on a die is 1 favorable outcome out of 6, so the probability is 1/6 ≈ 0.167, or about 16.7%.
For two independent events — where one has no effect on the other — 'both' multiplies the two probabilities, P(A and B) = P(A)·P(B). 'Either' adds them and subtracts the overlap, P(A or B) = P(A) + P(B) − P(A)·P(B).
'Neither' flips both to their opposites and multiplies: (1 − P(A)) · (1 − P(B)). Two coin flips landing heads is 0.5 × 0.5 = 0.25 for both, 0.75 for at least one, and 0.25 for neither.
Frequently asked questions
What does independent mean here?
Two events are independent when one happening doesn't change the odds of the other — like separate coin flips or dice rolls. The combined formulas assume that. If the events influence each other, they don't apply directly.
Should I enter probabilities as decimals or percentages?
Use decimals between 0 and 1 for the two-event section — 0.5 for a coin, 0.25 for a one-in-four chance. The single-event section takes raw outcome counts and hands back both the decimal and the percentage for you.
Why is 'either' not just P(A) plus P(B)?
Because straight addition double-counts the case where both happen. Subtracting P(A)·P(B) removes that overlap so you don't end up with a probability above 1. It's the classic inclusion-exclusion fix.
Can a probability be more than 1?
No — a valid probability runs from 0 (impossible) to 1 (certain). If you enter favorable outcomes greater than the total, or a value outside 0 to 1, the tool shows a dash rather than an answer that can't exist.