juniorProbability
What is the difference between independent and dependent events?
Updated May 17, 2026
Short answer
Independent events do not affect each other’s probabilities, while dependent events do.
Deep explanation
Two events A and B are independent if P(A ∩ B) = P(A)P(B). If the occurrence of one event changes the probability of the other, they are dependent. Dependency is common in real-world systems like conditional processes.
Real-world example
Drawing cards from a deck without replacement creates dependent events.
Common mistakes
- Assuming all sequential events are independent.
Follow-up questions
- How do you test independence?
- Can events be partially dependent?