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Independent event probabilities Calculator

Calculate intersections, unions and repeat-trial success chances. This free independent event probabilities calculator shows the calculation and its assumptions so you can compare your own figures.

Calculated on your device

Your results

Both Events Percent6%

Calculate intersections, unions and repeat-trial success chances.

At Least One AIn Trials Percent89.2626%

Calculated outcomes

Either Event Percent
44%
Neither Event Percent
56%

Assumptions and estimates

  • A and B must be independent for the product and union formulas. Repeated trials must be independent with identical probability of A. Zero trials means zero chance of at least one success. Real events often violate independence.
  • Method: Independent events: P(A and B)=ab, P(A or B)=a+b−ab; at least one A in n trials = 1−(1−a)^n.
  • Editable inputs are planning assumptions; check the method and result notes for scope.

Useful next steps

  1. Use Compare options to test an alternative side by side.
  2. Copy, print or download a record of this calculation when you need one.

Reports open your email app addressed to s@s1.ie with the public page address only. Your inputs are never added.

How the independent event probabilities calculation works

Independent events: P(A and B)=ab, P(A or B)=a+b−ab; at least one A in n trials = 1−(1−a)^n.

Editable inputs are planning assumptions; check the method and result notes for scope.

Using this calculator

  1. Enter your own figures in the labelled inputs. Keep the currencies, units and time periods consistent.
  2. Choose any applicable rate profile, pattern or assumption shown for this tool. Open additional inputs when relevant.
  3. Review both events percent and at least one ain trials percent, then read the stated assumptions and eligibility conditions before using the result.

Worked example

This is a static example using illustrative inputs, not facts about you or today’s date. The displayed eligibility selections and assumptions apply only to this example.

See example inputs
Chance of event A (%)
20
Chance of event B (%)
30
Independent trials of event A
10
Both Events Percent
6%
At Least One AIn Trials Percent
89.2626%

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