Probability Calculator

Two calculators: one turns “favorable out of possible” into a probability, the other combines two independent events.

Probability of a single event

Probability0.16666667 (16.666667%)
As a fraction
1/6
Probability it does not happen
0.83333333 (83.333333%)
Odds for : against
1 : 5

Working

  1. P = favorable outcomes ÷ total outcomes = 1 ÷ 6 = 0.16666667

Two independent events

A decimal (0.5) or a percentage (50%).

Fractions such as 1/6 also work.

P(A and B)0.08333333 (8.333333%)
P(A or B)
0.58333333 (58.333333%)
P(exactly one of A, B)
0.5 (50%)
P(neither A nor B)
0.41666667 (41.666667%)
P(not A)
0.5 (50%)
P(not B)
0.83333333 (83.333333%)

Working

  1. P(A and B) = P(A) × P(B) = 0.5 × 0.1666666667 = 0.08333333
  2. P(A or B) = P(A) + P(B) − P(A and B) = 0.58333333

These results assume A and B are independent: one happening does not change the chance of the other.

Basic probability

P(event) = favorable outcomes ÷ total outcomes

This assumes every outcome is equally likely, like the faces of a fair die. Probabilities run from 0 (impossible) to 1 (certain), and can be written as decimals, fractions or percentages.

Combining independent events

P(A and B) = P(A) × P(B)

P(A or B) = P(A) + P(B) − P(A) × P(B)

P(neither) = (1 − P(A)) × (1 − P(B))

P(not A) = 1 − P(A)

Events are independent when one does not affect the other — two coin tosses, or a coin toss and a die roll. Drawing cards without putting them back is not independent.

Worked example

A coin lands heads and a die shows 6

  1. P(heads) = 1/2 and P(six) = 1/6
  2. Both: 1/2 × 1/6 = 1/12 ≈ 0.0833
  3. At least one: 1/2 + 1/6 − 1/12 = 7/12 ≈ 0.5833

There is about an 8.3% chance of both and a 58.3% chance of at least one.

Probability and odds

Odds compare favorable to unfavorable outcomes. A probability of 1/6 corresponds to odds of 1 : 5 (one way to win, five ways to lose). The single-event calculator shows both.