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Math

Probability Calculator

Instantly calculate event probabilities — AND, OR, and complement rules

Calculation Mode

Event Probability

Enter values as decimals (0.5), fractions (1/6), or percentages (50%).

Result

P(A)0.550%
P(A) — event occurs50%
P(not A) — event does not occur50%
P(A)
0.5
P(A) as percentage
50%
P(not A) — complement

50%

0.5
Odds in favour of A
1 : 1

Probability Formulas

Complement Rule

P(not A) = 1 − P(A)

The probability that an event does NOT occur.

AND — Independent Events

P(A and B) = P(A) × P(B)

Both events occur; valid only when A and B are independent.

AND — Dependent Events

P(A and B) = P(A) × P(B|A)

Use when the outcome of A affects the probability of B.

OR — General (Inclusion-Exclusion)

P(A or B) = P(A) + P(B) − P(A∩B)

At least one of A or B occurs; subtracts the overlap.

OR — Mutually Exclusive

P(A or B) = P(A) + P(B)

Events cannot both happen at the same time, so P(A∩B) = 0.

Odds In Favour

Odds = P(A) : P(not A)

Ratio of success to failure; e.g. "3 : 2" means 3 wins per 2 losses.

About

A probability calculator helps you find the likelihood of events occurring — whether you need to know the chance of a single outcome, both events happening together (AND), at least one event occurring (OR), or the complement (the chance something does NOT happen). Enter any value as a decimal, fraction, or percentage and get instant results with visual probability bars.

FAQ
How do I calculate the probability of two independent events both occurring?+

Multiply their individual probabilities: P(A and B) = P(A) × P(B). For example, rolling a 6 on a die (1/6) AND flipping heads on a coin (1/2) gives 1/12 ≈ 0.083. Select the 'Both Events' mode and choose 'Independent events'.

What is the complement of a probability?+

The complement P(not A) = 1 − P(A). It represents the probability that an event does NOT happen. If P(rain today) = 0.3, then P(no rain) = 0.7.

When do I use the inclusion-exclusion formula for OR?+

Use P(A or B) = P(A) + P(B) − P(A∩B) whenever events can overlap (i.e., they are not mutually exclusive). If drawing a card that is a Heart OR a Queen, the Queen of Hearts is counted in both, so it must be subtracted once.

Can I enter probabilities as fractions or percentages?+

Yes. The calculator accepts decimals (0.25), fractions (1/4), and percentages (25%) interchangeably for all inputs.

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