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Probability & Counting

Probability Calculator

Pick the situation you are in. For a single event, give the favourable and total outcomes. For two independent events, give each probability as a decimal, fraction or percent.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Probabilities: 0.25, 1/4 or 25%
Try an example:
Answer1/6 = 16.6667%
  • Decimal: 0.166667
  • Odds against: 5 to 1
Step-by-step working 3 steps
  1. 1
    Favourable ÷ total
    P = 1 / 6 = 1/6

    Assumes every outcome is equally likely.

  2. 2
    As decimal and percent
    0.166667  =  16.6667%
  3. 3
    Probability of NOT happening
    1 − 0.166667 = 0.833333

How to use the probability calculator

  1. Choose the question type.
  2. Enter whole-number outcomes, or probabilities between 0 and 1.
  3. Read the answer as a percent and decimal.
  4. Check the assumption note in the first step.

Probability rules

P(event) = favourable / total
P(A and B) = P(A) × P(B)   (independent)
P(A or B) = P(A) + P(B) − P(A and B)
P(not A) = 1 − P(A)

Independence means one event does not change the other’s chance — like separate coin flips, but not cards drawn without replacement.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

Rolling a 6
Answer1/6 = 16.6667%
  • Decimal: 0.166667
  • Odds against: 5 to 1
Step-by-step working 3 steps
  1. 1
    Favourable ÷ total
    P = 1 / 6 = 1/6

    Assumes every outcome is equally likely.

  2. 2
    As decimal and percent
    0.166667  =  16.6667%
  3. 3
    Probability of NOT happening
    1 − 0.166667 = 0.833333
Two heads in a row
Answer25%
  • Decimal: 0.25
Step-by-step working 2 steps
  1. 1
    Read the two probabilities
    P(A) = 0.5,  P(B) = 0.5

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

  2. 2
    Multiply
    P(A and B) = P(A) × P(B) = 0.5 × 0.5 = 0.25
50% or 1/6, either
Answer58.3333%
  • Decimal: 0.583333
Step-by-step working 2 steps
  1. 1
    Read the two probabilities
    P(A) = 0.5,  P(B) = 0.166667

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

  2. 2
    Add, then remove the overlap
    P(A or B) = P(A) + P(B) − P(A and B)
= 0.5 + 0.166667 − 0.083333 = 0.583333

    Without subtracting the overlap, outcomes where both happen would be counted twice.

Drawing a heart
Answer1/4 = 25%
  • Decimal: 0.25
  • Odds against: 39 to 13
Step-by-step working 3 steps
  1. 1
    Favourable ÷ total
    P = 13 / 52 = 1/4

    Assumes every outcome is equally likely.

  2. 2
    As decimal and percent
    0.25  =  25%
  3. 3
    Probability of NOT happening
    1 − 0.25 = 0.75

Common mistakes to avoid

Multiplying when events are not independent

Drawing two cards without replacement changes the second probability. The simple product no longer applies.

Adding probabilities for “or” without subtracting the overlap

Outcomes where both happen get counted twice unless you subtract P(A and B).

Treating all outcomes as equally likely

favourable ÷ total only holds when each outcome has the same chance.

Frequently asked questions

What does independent mean?

Knowing one event happened tells you nothing about the other. Two separate dice rolls are independent.

Can probabilities be entered as percentages?

Yes — 25%, 0.25 and 1/4 are all accepted.