Probability Calculator

Work out the probability of an event and its complement, combine two events that are independent, mutually exclusive or have a known overlap, and find P(A and B), P(A or B) and P(A | B). Count permutations and combinations exactly, even for large n, and compute binomial probabilities P(X = k), P(X ≤ k) and P(X ≥ k) with a chart of the distribution.

How to use the Probability Calculator

1. Choose Single event, Two events, nPr / nCr or Binomial.
2. Enter probabilities as decimals, percentages or fractions.
3. Press Calculate.
4. Copy the results, and for binomial problems read the distribution chart.

Features

• P(A), P(not A) and odds
• Independent, mutually exclusive or known-overlap events
• Conditional probability P(A | B) and P(B | A)
• Exact permutations and combinations with big integers
• Binomial P(X = k), cumulative probabilities, mean and SD

Benefits

• Check probability homework and exam practice
• Exact counting results for lotteries and card hands
• Validates inputs that cannot be true probabilities

Frequently asked questions

What is the difference between permutations and combinations?

Permutations count ordered arrangements (nPr = n!/(n − r)!), while combinations count selections where order does not matter (nCr = n!/(r!(n − r)!)).

When are two events independent?

When one happening does not change the probability of the other, so P(A and B) = P(A) × P(B). Mutually exclusive events cannot happen together, so P(A and B) = 0.

What does the binomial distribution model?

The number of successes in n independent trials that each succeed with the same probability p, such as heads in 10 coin flips.

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