Probability formulas: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
The probability formulas are P(A or B) = P(A) + P(B) − P(A and B), and P(not A) = 1 − P(A).
What each letter means
- \(A\cup B\) A or B (or both)
- \(A\cap B\) A and B
- \(A'\) not A
When to use it
To combine probabilities of events: 'or' questions, 'at least one' questions, and Venn diagrams.
Worked example
\(P(A)=0.35\), \(P(B)=0.5\) and \(P(A\cap B)=0.2\). Find \(P(A\cup B)\) and the probability that neither happens.
- \(P(A\cup B)=0.35+0.5-0.2\)
- \(P(\text{neither})=1-0.65\)
Answer: \(P(A\cup B)=0.65\); \(P(\text{neither})=0.35\)
Common mistake
Adding the probabilities of events that can happen together without subtracting the overlap P(A ∩ B).
On your course
| Course | In the exam |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AA SL probability questions
- Practise AI SL Venn diagrams and probability questions
- Revise Probability (AA SL)
- Print AA SL one-page formula sheet
Questions
What is the probability formula?
The probability formulas are P(A or B) = P(A) + P(B) − P(A and B), and P(not A) = 1 − P(A). A∪ B: A or B (or both); A∩ B: A and B; A': not A.
Is the probability formulas given in the exam?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB Maths formula sheets; your teacher has the official booklet.
When can I just add probabilities?
When the events are mutually exclusive (they cannot both happen). Then P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B).
Our own wording, examples and card, checked by IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.