Probability of two events
Give the chance of A and of B in %, then say how they are linked. Nothing is assumed for you.
Result
20%A and B
- A or B (at least one)
- 70%
- Exactly one
- 50%
- Neither
- 30%
- Not A
- 50%
- Not B
- 60%
- A given B
- 50%
- B given A
- 40%
Inputs
- Link between A and B
- Independent
- Probability of A
- 50
- Probability of B
- 40
How it is calculated
Independent: P(A and B) = P(A) × P(B).
Result
A and B
- A or B (at least one)
- 70%
- Exactly one
- 50%
- Neither
- 30%
How it is calculated
- Independent: P(A and B) = P(A) × P(B).
- Mutually exclusive: P(A and B) = 0 (they cannot happen together).
- P(A or B) = P(A) + P(B) − P(A and B). Exactly one = P(A or B) − P(A and B).
- P(A given B) = P(A and B) ÷ P(B).
Example
Heads (50%) and rain (40%), independent: both = 20%, at least one = 70%.
Good to know
- Choosing “independent” when it is not true gives a wrong answer.
- With “I know A and B”, the value must be possible: between P(A) + P(B) − 100% and the smaller of the two.
Frequently asked questions
What is this tool used for?
Give the chance of A and of B in %, then say how they are linked. Nothing is assumed for you.
How is the result calculated?
Independent: P(A and B) = P(A) × P(B).
What should I check before using the result?
Choosing “independent” when it is not true gives a wrong answer.