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Calculation Machine

Probability Calculator

Combined probability of independent events.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
Both A and B
13.5%
A or B (either)
61.5%
Neither
38.5%
A at least once in 5 trials
83.193%
Odds of A
0.429 to 1

Quick answer

For independent events, P(A and B) = P(A)·P(B) and P(A or B) = P(A) + P(B) − P(A)·P(B).

The formula

P(A∩B) = P(A)·P(B)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Probability of A30 %
  • Probability of B45 %
  • Repeated trials of A5

Result

  • Both A and B13.5%
  • A or B (either)61.5%
  • Neither38.5%
  • A at least once in 5 trials83.193%
  • Odds of A0.429 to 1

How to use the Probability Calculator

  1. 1Enter the probability of each event as a percentage.
  2. 2Set repeated trials if you want the 'at least once' figure.
  3. 3Read the combined probabilities.

Frequently asked questions

What does independent mean?

One event's outcome doesn't change the other's probability. Two coin flips are independent; drawing cards without replacement is not.

Why is 'at least once' so high?

Failure has to happen every single time, and (1−p)^n shrinks fast — a 10% chance over 20 tries is 88% likely to occur.

About this calculator