Probability of Multiple Events
When dealing with three events, there are several probability scenarios to consider: all three occurring, at least one occurring, none occurring, exactly one, or exactly two. The calculations differ depending on whether events are independent (one event does not affect another) or mutually exclusive (events cannot occur simultaneously).
This calculator handles both independent and mutually exclusive events. For independent events, the probability of all three occurring is simply the product of individual probabilities. For mutually exclusive events, the probability of at least one occurring is the sum, and the probability of all three is zero.
Formulas for Three Events
Independent Events
Mutually Exclusive Events
Scenario Comparison
| Scenario | Independent Formula | Result (0.5, 0.3, 0.4) |
|---|---|---|
| All three | P(A)×P(B)×P(C) | 0.060 |
| None | (1-A)(1-B)(1-C) | 0.210 |
| At least one | 1 - P(none) | 0.790 |
| Exactly one | Sum of single-only | 0.440 |
Frequently Asked Questions
What if the events are not independent?
If events are dependent, you need conditional probabilities. The formula becomes P(A∩B∩C) = P(A) × P(B|A) × P(C|A∩B). This calculator assumes independence or mutual exclusivity. For dependent events, you would need to know the conditional probabilities.
Can three events be both independent and mutually exclusive?
Only in the trivial case where at least two of the events have probability zero. In general, if P(A) > 0 and P(B) > 0, and A and B are mutually exclusive, then P(A∩B) = 0, but P(A)×P(B) > 0, so they cannot be independent.