Free · Probability and statistical models

Independent Events Intersection and Related Chances

Calculate both-event probability and the associated union, complements and exclusive outcomes.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Independent events with chances 20% and 50% both occur with chance 10%.

P(A∩B)=P(A)P(B); P(A∪B)=P(A)+P(B)−P(A)P(B)

Worked example

Enter these known values and leave the other values blank.

Probability of A, P(A): 20 %
Probability of B, P(B): 50 %

P(A∩B): 10 %

Assumptions and limitations

All formulas here assume the two events are independent.
Use probabilities from 0 through 1, or percentages from 0 through 100. Complements share the same sample space.

Common questions

Which assumptions govern this model?

All formulas here assume the two events are independent.

References

Replace captured external image with an original accessible description preserving its complete probability/count relationships and all variant conditions.

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