Mutually Exclusive Events Calculator

Work out mutually exclusive events instantly with clear inputs, formula shown and shareable results.

About Mutually Exclusive Events Calculator

Mutually exclusive events cannot occur together, so their intersection is empty and P(A or B) is simply P(A) + P(B). Their probabilities can never sum to more than 1.

Formula

Exclusive union

P(A ∪ B) = P(A) + P(B) when A ∩ B = ∅

Worked example

With the default values below, Mutually Exclusive Events Calculator returns P(A or B) of 0.75000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Probability of Aaccepts 0–100 %: 30 %
Probability of Baccepts 0–100 %: 45 %

Results

P(A or B): 0.75000000
P(A and B) — always zero: 0.00000000
P(neither): 0.25000000
Ratio of P(A) to P(B): 0.66666667

Step by step

1Values used
2Exclusive union
3P(A or B)= 0.75000000
4P(A and B) — always zero= 0.00000000
5P(neither)= 0.25000000
6Ratio of P(A) to P(B)= 0.66666667

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For P(A) = 0.3 and P(B) = 0.45?

Either occurs with probability 0.75 and neither with 0.25.

Can exclusive events be independent?

Only if one has probability zero. Otherwise knowing A occurred tells you B definitely did not, which is dependence.