Combine the probabilities of two independent events: both happening, at least one, exactly one, neither, and each not happening.
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With probability of a (%) 50, probability of b (%) 30, the both a and b is 15%.
| Probability of A (%) | 50 |
|---|---|
| Probability of B (%) | 30 |
| Both A and B | 15% |
|---|---|
| A or B (at least one) | 65% |
| Not A | 50% |
| Not B | 70% |
| Exactly one of A or B | 50% |
| Neither A nor B | 35% |
Enter each event's probability as a percentage. Two events are independent when one happening does not change the chance of the other, like two coin tosses or two dice. The calculator applies the multiplication rule and the addition rule to give every combined outcome. If the events affect each other, these results do not apply.
P(A and B) = P(A) × P(B). P(A or B) = P(A) + P(B) − P(A)P(B). P(not A) = 1 − P(A). Enter each event's probability as a percentage. Two events are independent when one happening does not change the chance of the other, like two coin tosses or two dice. The calculator applies the multiplication rule and the addition rule to give every combined outcome. If the events affect each other, these results do not apply.
With probability of a (%) 50, probability of b (%) 30, the both a and b is 15%. A or B (at least one): 65%; Not A: 50%; Not B: 70%; Exactly one of A or B: 50%; Neither A nor B: 35%.
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Each toss has a 50% chance, and the tosses are independent, so P(both) = 0.5 × 0.5 = 25%.
Adding P(A) and P(B) counts the outcomes where both happen twice. Subtracting the overlap once gives the true chance that at least one happens.
Find the chance of no successes and subtract it from 1. With a 30% chance per try, three independent tries give 1 − 0.7³ = 65.7%.