Probability Calculator

Combine the probabilities of two events: both, either, neither and exactly one.

P(A)	0.5
P(B)	0.4
A and B are	Independent

P(A)

P(B)

A and B are

P(A or B)

0.7 (70%)

For independent events, P(A and B) = P(A) × P(B).

P(A and B): 0.2 (20%)
P(A or B): 0.7 (70%)
P(not A): 0.5 (50%)
P(not B): 0.6 (60%)
P(neither): 0.3 (30%)
P(exactly one): 0.5 (50%)

The events as a Venn diagram

Circle sizes are illustrative; the numbers are the probabilities of each region.

Simulation: the relative frequency of “A or B” in 2,000 trials settles near 0.7

Point at the curvePoint at the chart, or Tab to it and use ← →

relative frequencyprobability

About the Probability Calculator

Independent events don't affect each other (two coin flips). Mutually exclusive events can't happen together (rolling a 2 and a 5 on one die). The rules for combining them differ, so choose the right relationship.

The formula

P(A or B) = P(A) + P(B) − P(A and B)

Independent: P(A and B) = P(A) × P(B)
Mutually exclusive: P(A and B) = 0
Complement: P(not A) = 1 − P(A)

Worked example

Two coins, P(heads) = 0.5 each

P(both heads) = 0.25
P(at least one head) = 0.75

Questions people ask

How do I enter a percentage?

As a decimal: 35% is 0.35.

What about events that are neither?

Then you need P(A and B) directly, from data or a conditional probability.