Probability Calculator
Find the chance that two independent events both happen, either happens or neither does, or the chance of k successes in a run of repeated trials.
For two independent events, multiply to get the chance both happen and use P(A) + P(B) - P(A and B) for the chance that at least one does. With A at 0.5 and B at 0.3, both happen 15% of the time, at least one 65%, and neither 35%. For repeated trials, the binomial formula gives the chance of exactly k successes in n tries.
Results assume the events or trials are independent and that the probabilities you enter are right. Real events are often linked, such as weather on back-to-back days, and then these figures can be far off. Results are rounded to two decimals of a percent.
A and B are treated as independent: one happening does not change the chance of the other.
Both A and B
15%
0.1500, 1 in 7
- A or B (at least one)
- 65% (0.6500, 1 in 2)
- Exactly one of them
- 50% (0.5000, 1 in 2)
- Neither
- 35% (0.3500, 1 in 3)
- A but not B
- 35% (0.3500, 1 in 3)
- B but not A
- 15% (0.1500, 1 in 7)
- Not A
- 50% (0.5000, 1 in 2)
- Not B
- 70% (0.7000)
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About the Probability Calculator
Two rules cover most everyday probability questions. If two events are independent, so one happening tells you nothing about the other, the chance that both happen is the product of their chances. The chance that at least one happens is the sum minus that overlap, because adding the two would count the both-happen case twice. Two fair coins both land heads with probability 0.5 times 0.5, or 25%. Two dice both show a six 1 time in 36, about 2.78%. The repeated-trials mode applies the same multiplication over many tries. The chance of no success in n tries is the failure chance raised to the power n, so the chance of at least one is one minus that: rolling a die four times gives at least one six 51.77% of the time. For exactly k successes, the binomial formula counts the ways to place the k successes among the n tries and multiplies by the chance of each arrangement. Ten coin flips land exactly five heads 24.61% of the time. Inputs can be a decimal, a percent or a fraction such as 1/6, and every result is worked out exactly before it is rounded.
Frequently asked questions
How do I calculate the probability of A and B?+
When A and B are independent, multiply them: P(A and B) = P(A) x P(B). A 50% chance and a 30% chance give 0.5 x 0.3 = 0.15, or 15%. If one event changes the chance of the other, you need the conditional probability instead, which this calculator does not take.
How do I calculate the probability of A or B?+
Add the two and subtract the chance that both happen: P(A or B) = P(A) + P(B) - P(A and B). With 0.5 and 0.3 that is 0.5 + 0.3 - 0.15 = 0.65, so at least one of them happens 65% of the time.
What is the probability of at least one success?+
One minus the chance of failing every time. If a part is defective 2% of the time, a batch of 100 has no defective part with probability 0.98 to the power 100, about 13.26%, so at least one is defective 86.74% of the time.
Can I enter a chance like 1 in 6?+
Enter it as the fraction 1/6, or as 0.1667 or 16.67%. Each result also shows its 1 in X form: set both events to 1/6 and the chance of two sixes on two dice reads 2.78%, or 1 in 36.
Rules for independent events: OpenStax, Introductory Statistics 2e, section 3.3. Repeated trials: NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.6.18 Binomial Distribution.
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