OR Probability Calculator

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Independent events can both happen at the same time (e.g. rolling a 3 and rolling an odd number). Mutually exclusive events cannot both happen (e.g. rolling a 3 and rolling a 4 on the same single die roll).
Enter a value between 0 and 1. For example, enter 0.25 for a 25% probability.
Enter a value between 0 and 1. For example, enter 0.5 for a 50% probability.
P(A or B) - at least oneModerate
0.58%

Probability that event A occurs, event B occurs, or both occur (inclusive OR / union).

P(A and B) - both0.12%
P(A XOR B) - exactly one0.46%
P(neither) - neither occurs0.42%
P(A') - A does not occur0.6%
P(B') - B does not occur0.7%
At least one (A or B)0.58%
Both (A and B)0.12%
Exactly one (XOR)0.46%
Neither0.42%

There is a 58.00% chance that at least one event occurs.

  • P(A and B) = P(A) x P(B) = 40.00% x 30.00% = 12.00%.
  • The union P(A or B) = 40.00% + 30.00% - 12.00% = 58.00% (subtracting the overlap avoids double-counting).
  • The probability that neither A nor B occurs is 42.00%, which is the complement of P(A or B).

Next stepUse the XOR figure (exactly one) if you need to distinguish scenarios where one event succeeds but the other does not.

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