What Is the Independent Events Probability Calculator?
This calculator works out the combined probability of two independent events, A and B. Two events are independent when the occurrence of one has no effect on the probability of the other — for example, flipping a coin and rolling a die. Enter each individual probability and instantly get the chance that both happen, that at least one happens, and that neither happens.
How to Use It
Enter the probability of event A and event B as numbers between 0 and 1 (a probability of 50% is 0.5). Click calculate. The tool returns:
- P(A and B) — both events occur.
- P(A or B) — at least one event occurs.
- P(neither) — neither event occurs.
The Formula Explained
For independent events the joint probability is simply the product of the individual probabilities:
The probability that at least one event happens uses the inclusion–exclusion rule, where the overlap is the product because the events are independent:
The probability that neither happens is the product of the complements:
Worked Example
Suppose P(A) = 0.5 and P(B) = 0.4. Then:
- P(A \cap B) = 0.5 × 0.4 = 0.20
- P(A \cup B) = 0.5 + 0.4 - 0.20 = 0.70
- P(neither) = (1 - 0.5)(1 - 0.4) = 0.5 × 0.6 = 0.30
Notice P(A \cup B) + P(neither) = 0.70 + 0.30 = 1.00, a useful sanity check.
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