Pythagorist
Statistics

Probability Calculator

Calculate the theoretical probability of an event. Enter the number of favourable outcomes and the total outcomes to get the probability as a fraction, decimal, and percentage.

Fraction

3/10

Decimal

0.3

Percentage

30%

How it works

  1. Write probability as a fraction

    P=favourable outcomestotal outcomes=310P = \frac{\text{favourable outcomes}}{\text{total outcomes}} = \frac{3}{10}

    3 favourable outcomes out of 10 total outcomes.

  2. Simplify the fraction

    310=310\frac{3}{10} = \frac{3}{10}

    Divide numerator and denominator by their GCD (1).

    Result:3/10

  3. Convert to decimal and percentage

    3÷10=0.3=30%3 \div 10 = 0.3 = 30\%

    Divide numerator by denominator: 0.3. Multiply by 100: 30%.

    Result:0.3 = 30%

Theoretical Probability

P(event)=number of favourable outcomestotal number of outcomesP(\text{event}) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}
P(event)P(event)Probability of the event occurring (0 to 1)
favourablefavourableNumber of outcomes that satisfy the condition
totaltotalTotal number of equally likely outcomes

Example substitution

P(red)=310=0.3=30%P(\text{red}) = \frac{3}{10} = 0.3 = 30\%

3 red balls out of 10 total: probability = 3/10 = 0.3 = 30%.

Worked examples

A bag contains 4 blue balls, 3 red balls, and 5 green balls. What is the probability of picking a red ball?

  1. 1
    Count favourable outcomes: 3 red balls
  2. 2
    Count total outcomes: 4 + 3 + 5 = 12 balls total
  3. 3
    Write as a fraction: P(red) = 3/12
  4. 4
    Simplify: 3/12 = 1/4 = 0.25 = 25%
Answer: P(red) = 1/4 = 0.25 = 25%

A fair dice is rolled. What is the probability of rolling a number greater than 4?

  1. 1
    Favourable outcomes: 5 and 6 → 2 favourable outcomes
  2. 2
    Total outcomes: 6 faces on a dice
  3. 3
    Calculate probability: P(>4) = 2/6 = 1/3 ≈ 0.333 = 33.3%
Answer: P(>4) = 1/3 ≈ 33.3%

Frequently asked questions

What is the formula for probability?+

P(event) = number of favourable outcomes / total number of possible outcomes.

What is P(A and B)?+

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

What is P(A or B)?+

P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events: P(A or B) = P(A) + P(B).

What is complementary probability?+

P(not A) = 1 − P(A). The probability of something not happening equals 1 minus the probability it does happen.

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