Probability Calculator

Probability questions appear in Class 10 and 12 maths, in aptitude tests for banking and SSC exams, and in everyday decisions. This probability calculator covers the common cases: the chance of a single event, the chance of two events happening together or either one (including conditional probability), thebinomial chance of exactly k successes in n tries, the chance of something happening at least once, and counting with combinations and permutations. Each answer is shown as a fraction-friendly decimal, a percentage and odds.

How to use it

Pick the type of problem.
Fill in the values; type probabilities as decimals, fractions or percentages.
Read the answer and the related probabilities below it.

Example

What's the chance of rolling at least one six in 4 throws of a die? It's easier to work out the opposite: no six in 4 throws is (5/6)⁴ ≈ 48.2%, so at least one six is 1 − 0.482 ≈ 51.8% — just better than even, a puzzle famous since the 1600s. And choosing a team of 3 from 11 players can be done in11C3 = 165 ways. Pick random winners fairly with the random name picker.

Frequently asked questions

How do I calculate a probability?

Probability = favourable outcomes ÷ total equally likely outcomes. The chance of rolling a 6 on a die is 1 ÷ 6 ≈ 16.7%. Probabilities are always between 0 (impossible) and 1 (certain).

What is the difference between “and” and “or”?

P(A and B) is the chance both happen; for independent events it is P(A) × P(B). P(A or B) is the chance at least one happens: P(A) + P(B) − P(A and B), so the overlap isn’t counted twice.

What is the binomial distribution?

It gives the chance of exactly k successes in n independent tries, each with the same chance p: nCk × pᵏ × (1 − p)ⁿ⁻ᵏ. For example, exactly 5 heads in 10 coin tosses has probability 252 ÷ 1024 ≈ 24.6%.

What is the difference between nCr and nPr?

nCr (combinations) counts selections where order doesn’t matter — choosing 3 players from 11. nPr (permutations) counts arrangements where order matters — gold, silver and bronze from 11 runners. nPr = nCr × r!.

What are odds?

Odds compare favourable to unfavourable outcomes. A 1 in 6 chance is odds of 1 : 5 in favour (or 5 : 1 against).