Probability Rules: And, Or, Independent Events
Use the addition and multiplication rules for probability, and know when events are independent or mutually exclusive, with two worked examples.
The two rules
- OR: P(A or B) = P(A) + P(B) − P(A and B)
- AND (independent): P(A and B) = P(A) × P(B)
Mutually exclusive events have P(A and B) = 0.
Tell them apart
- Independent: one does not change the other
- Mutually exclusive: they cannot both happen
- Exclusive events have P(A and B) = 0
Independent and mutually exclusive are different ideas.
Example 1
Flip a coin and roll a die. What is P(heads and a 6)?
- The two are independent
- P(heads) = 1/2 and P(6) = 1/6
- Multiply: 1/2 × 1/6
1/12 ≈ 0.083
Example 2
P(A) = 0.5, P(B) = 0.25, P(A and B) = 0.1. Find P(A or B).
- Add: 0.5 + 0.25 = 0.75
- Subtract the overlap: 0.75 − 0.1
P(A or B) = 0.65
Common mistake
P(A or B) = P(A) + P(B) always
You must subtract P(A and B) so the overlap is not counted twice.
Only mutually exclusive events skip the subtraction.
Multiplication needs independence.
Want more Statistics practice?
The free Statistics study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.
Open the Statistics guide