Probability Calculator

Work out a probability from favourable and total outcomes, or combine two independent events (A and B, A or B, neither, exactly one).

The outcomes you want, e.g. 3 red balls
All equally likely outcomes

Result

Enter values and press Calculate to see the result.

Formula

P(E)=favourable outcomestotal outcomesP(E) = \frac{\text{favourable outcomes}}{\text{total outcomes}}

For equally likely outcomes.

P(not E)=1−P(E)P(\text{not } E) = 1 - P(E)

The complement: the event does not happen.

P(A∩B)=P(A) P(B)P(A \cap B) = P(A)\,P(B)

Both happen, when A and B are independent.

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

At least one happens.

How to use this calculator

  1. For one event, enter how many outcomes you want and how many there are in total.
  2. For two independent events, enter each probability as a fraction (1/2) or a decimal (0.5).

Worked example

3 red balls in a bag of 8

P(red) = 3/8 = 0.375 = 37.5%.

P(not red) = 1 − 3/8 = 5/8.

The odds of red are 3 : 5 (3 for, 5 against).

Frequently asked questions

What does independent mean?

One event does not change the chance of the other — like two separate coin flips.

What is the difference between probability and odds?

Probability compares favourable outcomes with all outcomes (3/8); odds compare favourable with unfavourable (3 : 5).