Calculateur de Probabilité d'Union
Calculez la probabilité de l'union de deux événements.
P(A or B)
0.700000
P(A or B) vs P(A)
Formule
How to Calculate Union Probability
Formula
P(A or B) = P(A) + P(B) - P(A and B)
The addition rule accounts for the overlap between events A and B. If you simply add P(A) and P(B), the intersection is counted twice, so you subtract P(A and B) once. For mutually exclusive events, P(A and B) = 0.
Exemple Résolu
P(A) = 0.3, P(B) = 0.5, P(A and B) = 0.1. Find P(A or B).
- 01P(A or B) = P(A) + P(B) - P(A and B)
- 02P(A or B) = 0.3 + 0.5 - 0.1
- 03P(A or B) = 0.7
- 04P(Neither) = 1 - 0.7 = 0.3
Questions Fréquentes
What if the events are mutually exclusive?
If A and B cannot occur together, P(A and B) = 0, so P(A or B) = P(A) + P(B). This is the special addition rule.
Can P(A or B) exceed 1?
No. If your calculation gives a value above 1, check that P(A and B) is not too small or that P(A) and P(B) are valid. The intersection must satisfy P(A and B) <= min(P(A), P(B)).
How does this extend to three events?
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C). This is the inclusion-exclusion principle.
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