Probability of the Union of Two Events
The probability of the union of two events depends on the probability of either event and the probability of only one of the events occuring.
The probability of A\[Union]B equals the sum of the probabilities of A and B minus the probability of A\[Intersection]B.
Formula
![QuantityVariable["P(A⋃B)", "Unitless"] == QuantityVariable["P(A)", "Unitless"] - QuantityVariable["P(A⋂B)", "Unitless"] + QuantityVariable["P(B)", "Unitless"]](https://www.wolframcloud.com/objects/resourcesystem/marketplacestorage/resources/1bc/1bca061c-f587-4092-bd64-4391d294f0c9/Webpage/FormulaImage.png "Copy to Clipboard")
| symbol | description | physical quantity |
|---|---|---|
| P(A⋃B) | probability of A⋃B |
"Unitless" |
| P(A) | probability of A |
"Unitless" |
| P(A⋂B) | probability of A⋂B |
"Unitless" |
| P(B) | probability of B |
"Unitless" |
Forms
Examples
Get the resource:
| In[1]:= | ![ResourceObject["Probability of the Union of Two Events"]](images/1bc/1bca061c-f587-4092-bd64-4391d294f0c9-io-1-i.en.gif){kind=small} |
| Out[1]= |  |
Get the formula:
| In[2]:= | ![FormulaData[ResourceObject["Probability of the Union of Two Events"]]](images/1bc/1bca061c-f587-4092-bd64-4391d294f0c9-io-2-i.en.gif){kind=small} |
| Out[2]= |  |
Use some values:
| In[3]:= | ![FormulaData[
ResourceObject[
"Probability of the Union of Two Events"], {QuantityVariable[
"P(B)","Unitless"] -> 0.6`,
QuantityVariable["P(A\[Union]B)","Unitless"] -> 0.7`}]](images/1bc/1bca061c-f587-4092-bd64-4391d294f0c9-io-3-i.en.gif){kind=small} |
| Out[3]= |  |