Probability Calculator
Calculate probability as fraction, decimal and percentage. Also compute combinations (nCr) and permutations (nPr) with step-by-step working.
Basic Probability
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Fraction
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Decimal
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Percentage
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Complement P(not A)
Combinations (nCr) and Permutations (nPr)
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nCr (Combinations)
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nPr (Permutations)
Step-by-Step
Frequently Asked Questions
What is probability?
Probability measures the likelihood of an event occurring. It is expressed as a value between 0 (impossible) and 1 (certain). P(event) = Favourable outcomes / Total outcomes. For example, rolling a 4 on a standard die: P = 1/6 ≈ 0.167 = 16.7%.
What is the difference between combinations (nCr) and permutations (nPr)?
Combinations (nCr) count the number of ways to choose r items from n items when order does NOT matter. Permutations (nPr) count the ways when order DOES matter. For example, choosing 3 students from a class of 30 for a team uses combinations; ranking 3 winners in a race uses permutations.
How do you calculate nCr?
nCr = n! / (r! × (n−r)!). For example, 5C2 = 5! / (2! × 3!) = 120 / (2 × 6) = 10. This means there are 10 ways to choose 2 items from 5.
How do you calculate nPr?
nPr = n! / (n−r)!. For example, 5P2 = 5! / 3! = 120 / 6 = 20. There are 20 ordered arrangements of 2 items chosen from 5.
How is probability used in everyday Nigerian life?
Probability is used in Nigerian sports betting (calculating odds), insurance (risk assessment), election predictions, lottery analysis, and business decision-making. Understanding probability helps in evaluating the true likelihood of events and making informed decisions.