Free · Probability and statistical models

Joint Probability with Conditional or Independent Inputs

Find the intersection probability from an independent pair or a conditional probability.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

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

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 40% conditional probability given B, with B at 50%, gives a 20% joint probability.

P(A∩B) = P(A|B)P(B); under independence P(A|B)=P(A)

Worked example

Enter these known values and leave the other values blank.

Are the events independent?
No, one depends on the other.
P(A|B)
40 %
P(B)
50 %
P(A and B)
20 %

Assumptions and limitations

  • Inputs must be probabilities from zero through one, or zero through 100 in percentage units.
  • Conditional probabilities require a specified conditioning event. Independence is an assumption in the independent mode.

Common questions

Which assumptions govern this model?

Inputs must be probabilities from zero through one, or zero through 100 in percentage units.

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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