How this calculation works
Adding the two probabilities counts their intersection twice. Subtract it once to recover the union.
THE FORMULA
P(A ∪ B) = P(A)+P(B)−P(A∩B)A worked example
0.4 + 0.5 − 0.2 = 0.7. Subtracting the overlap counts it once.
Good to know
The entered probabilities must describe events in the same sample space.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Find the probability of either event when their overlap is known.
The primary result is labeled “Probability of A or B”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The entered probabilities must describe events in the same sample space.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
0.4 + 0.5 − 0.2 = 0.7. Subtracting the overlap counts it once.
Which rule does this calculator apply?
P(A ∪ B) = P(A)+P(B)−P(A∩B)