Free · Probability and statistical models

Independent Events Union and Related Chances

Calculate the chance that at least one of two independent events occurs.

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 event chances 20% and 50% give a 60% chance of at least one occurring.

P(A∪B)=1−(1−P(A))(1−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): 60 %

Assumptions and limitations

Both events may occur together; the union counts their overlap once.
All formulas here assume independence and a shared sample space.

Common questions

Which assumptions govern this model?

Both events may occur together; the union counts their overlap once.

References

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

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