Probability calculator

Combine event probabilities using their overlap: P(A or B) = P(A) + P(B) − P(A and B).

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Probability P(A)

Probability P(B)

More inputs and assumptions

Intersection P(A and B)

Answer

…

Combine event probabilities using their overlap: P(A or B) = P(A) + P(B) − P(A and B).

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Saved scenario

Save the current answer, then change an input to compare. This clears when you leave.

Formula and assumptions

Enter the intersection explicitly; independence is not assumed. Probabilities range from 0 to 1, and impossible overlaps are rejected.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Probability calculator

Combine event probabilities using their overlap: P(A or B) = P(A) + P(B) − P(A and B).

Enter the intersection explicitly; independence is not assumed. Probabilities range from 0 to 1, and impossible overlaps are rejected.

Next: Basic calculator

A worked example

With probability p(a) = 0.5, probability p(b) = 0.4, intersection p(a and b) = 0.2, the probability a or b is 0.7.

Before you use the result

Enter the intersection explicitly; independence is not assumed. Probabilities range from 0 to 1, and impossible overlaps are rejected.

Example results for probability p(a)

These examples use Probability P(B): 0.4; Intersection P(A and B): 0.2. They are reference calculations, not recommended settings.

Probability P(A)	Probability A or B
0.25	0.45
0.5	0.7

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