justyourcalculatorProbability Calculator
Combine event probabilities or find a normal distribution range.
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Probability Calculator
Two events, repeated events and normal ranges
Between 0 and 1.
P(A and B), independent events
0.2
- P(A or B)at least one happens
- 0.7
- P(exactly one of A, B)A xor B
- 0.5
- P(neither A nor B)
- 0.3
- P(not both)
- 0.8
- P(A')A does not happen
- 0.5
- P(B')
- 0.6
- P(A and not B)
- 0.3
- P(B and not A)
- 0.2
Assumes A and B are independent (one happening doesn't change the chance of the other).
How it was calculated
- P(A ∩ B) = P(A) × P(B) = 0.5 × 0.4 = 0.2
- P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.5 + 0.4 - 0.2 = 0.7
- P(A Δ B) = P(A) + P(B) - 2P(A ∩ B) = 0.5
- P((A ∪ B)') = 1 - P(A ∪ B) = 0.3
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How the probability calculator works
Probability is a number from 0 (impossible) to 1 (certain). For two independent events, the chance both happen is P(A) × P(B), and the chance at least one happens is P(A) + P(B) - P(A) × P(B), which subtracts the overlap so it isn't counted twice.
For repeated independent trials, the chance of something happening every time is P^n, the chance it never happens is (1 - P)^n, and the chance it happens at least once is 1 - (1 - P)^n. That last one is why a 1-in-6 chance becomes a 66.5% chance over six tries.
The normal distribution tab converts bounds to z-scores, z = (x - μ) / σ, and uses the standard normal cumulative distribution Φ(z) to find the probability of a value landing between them.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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