Probability Calculator
Calculate the probability of two independent events happening together, either, or neither.
Assumptions used in this calculation
- Independence: Assumes events A and B are independent, the outcome of one doesn't affect the other.
About this calculator
Working out the odds of two things both happening, or at least one happening, is a common source of confusion because the correct approach depends on whether you multiply or add probabilities, and adding without subtracting the overlap double-counts the case where both happen. This calculator takes the probability of two independent events A and B, entered as favorable outcomes over total outcomes for each, and computes P(A and B) as P(A) × P(B), P(A or B) as P(A) + P(B) − P(A and B) to avoid double-counting the overlap, the probability of neither occurring, and the complement of A (the chance A doesn't happen). It assumes A and B are independent, meaning the outcome of one doesn't influence the other, which holds for something like a coin flip and a separate die roll but not for events like drawing cards without replacement. That handles the addition-vs-multiplication distinction and the double-counting correction that trip people up doing this arithmetic by hand.
Worked example
Coin heads (1/2) and rolling a 6 (1/6)
Result: P(both) ≈ 8.33%, P(either) ≈ 58.33%
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