Independent Events Calculator

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

About Independent Events Calculator

Independent events do not influence each other, so P(A and B) = P(A)·P(B). The union then follows from the addition rule with that product subtracted to avoid double counting.

Formulas

Independence

P(A ∩ B) = P(A)·P(B)

Union

P(A ∪ B) = P(A) + P(B) − P(A)P(B)

Worked example

With the default values below, Independent Events Calculator returns P(A and B) of 0.10000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Probability of Aaccepts 0–100 %: 40 %
Probability of Baccepts 0–100 %: 25 %

Results

P(A and B): 0.10000000
P(A or B): 0.55000000
P(neither): 0.45000000
P(exactly one): 0.45000000

Step by step

1Values used
2Independence
3Union
4P(A and B)= 0.10000000
5P(A or B)= 0.55000000
6P(neither)= 0.45000000
7P(exactly one)= 0.45000000

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) = 0.4 and P(B) = 0.25?

Both occur with probability 0.1, either with 0.55, neither with 0.45 and exactly one with 0.45.

How is independence different from exclusivity?

Independent events can both happen; mutually exclusive ones cannot. In fact exclusive events with positive probability are never independent.