Free · Probability and statistical models

Independent Events and Repeated Trial Chances

Compare independent event combinations and constant-probability sequences.

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

For p=20% over two independent trials, the chances are 4% for both, 64% for neither and 36% for at least one.

P(all n successes)=p^n; P(no successes)=(1−p)^n; P(at least one)=1−(1−p)^n

Worked example

Enter these known values and leave the other values blank.

Probability of A: P(A): 20 %
Probability of B: P(B): 50 %
Number of trials: 2

P(A∩B): 10 %
P(A): 20 %
Probability: 4 %

Assumptions and limitations

The paired events and repeated trials are independent with constant probability.
A sequence length must be a nonnegative integer. The zero-trial sequence has probability one for all or no successes and zero for at least one.

Common questions

Which assumptions govern this model?

The paired events and repeated trials are independent with constant probability.

References

Replace captured external image with an original accessible description preserving its complete probability/count relationships and all variant conditions. Enforce the mathematical input domain and include valid zero boundaries while preserving the captured arithmetic and control graph.

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