How this calculator works
Counting favourable outcomes works when every elementary outcome has equal probability. For two events, adding their probabilities double-counts their overlap, so subtract the joint probability once to obtain the union. Independence supplies that joint value as a product. Otherwise it must be provided or estimated. The calculator rejects overlaps that imply negative exclusive regions or a union above one.
Formula
P(A) = favourable/total for equally likely outcomes. P(A or B) = P(A) + P(B) - P(A and B). P(exactly one) = P(A) + P(B) - 2P(A and B). P(neither) = 1 - P(A or B).
Worked example
Two favourable outcomes among five give 40%. For independent events with probabilities 50% and 40%, both occur with probability 20%, at least one with 70%, neither with 30% and exactly one with 50%.
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Frequently asked questions
What does or mean here?
It is inclusive: A, B or both. Exactly one is provided separately.
Are mutually exclusive events independent?
Usually no. Two events with positive probabilities that cannot occur together are dependent.
Why reject an overlap smaller than P(A) + P(B) - 1?
Such an overlap would imply a union above 100%. It cannot belong to a valid probability model.