The Probability Calculator finds probabilities of two independent events, of repeated events, and of ranges in a normal distribution.
Assuming A and B are independent
| P(A') | 0.5 |
| P(B') | 0.6 |
| P(A∩B) | 0.2 |
| P(A∪B) | 0.7 |
| P(AΔB) | 0.5 |
| P((A∪B)') | 0.3 |
| A occurs all 5 times | 0.07776 |
| B occurs all 3 times | 0.027 |
| Both of the above | 0.0021 |
| A never occurs in 5 tries | 0.01024 |
| A occurs at least once | 0.98976 |
| B occurs at least once | 0.657 |
| P(-1 < X < 1) | 0.682689 |
| Outside this range | 0.317311 |
Probability measures how likely an event is, from 0 (impossible) to 1 (certain). The complement rule says P(not A) = 1 − P(A). For independent events, where one does not affect the other, P(A and B) = P(A) × P(B).
P(A∪B) = P(A) + P(B) − P(A∩B): add the probabilities and subtract the overlap so it is not counted twice. P(A or B but not both) = P(A) + P(B) − 2P(A∩B). P(neither) = 1 − P(A∪B).
Worked example (defaults): P(A) = 0.5 and P(B) = 0.4, independent. Both: 0.2. At least one: 0.7. Exactly one: 0.5. Neither: 0.3.
The probability that an independent event with probability p happens n times in a row is pⁿ. The chance it happens at least once in n tries is 1 − (1 − p)ⁿ. Five heads in a row with a fair coin: 0.5⁵ = 3.125%.
Many measurements cluster around a mean in a bell curve. About 68% of values lie within one standard deviation, 95% within two and 99.7% within three. The calculator integrates the curve between any two bounds.
What does independent mean? Knowing one outcome tells you nothing about the other.
What is the gambler's fallacy? Believing past results change independent future odds.
Can probability be more than 1? No.