Two independent events probability calculator
Enter the chance of event A and event B as percentages to get every common combination used in probability questions.
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How to use it
- Enter chance of a and chance of b.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
P(A and B) = P(A) × P(B). P(A or B) = P(A) + P(B) - P(A) × P(B). P(neither) = (1 - P(A)) × (1 - P(B)). P(exactly one) = P(A or B) - P(A and B).
Example
Inputs: Chance of A = 30 %, Chance of B = 60 %. Result: Both A and B: 18%; A or B (at least one): 72%; Neither A nor B: 28%.
Limits and caveats
- Only valid when the events are independent, so one happening does not change the chance of the other.
Questions about this tool
When are two events independent?
When neither affects the other, like a coin toss and a die roll. Drawing two cards without replacement is not independent.
Why not just add the chances for A or B?
Adding counts the both case twice, so P(A and B) is subtracted once.
What is the difference between independent and mutually exclusive?
Mutually exclusive events never happen together, so P(A and B) is zero. Independent events can happen together.