PEAZIT Aha card
Go straight to resources ↓Multiply probabilities for independent events
Independence means one trial's result does not change the other's chance. Multiply probabilities when both conditions must hold.
| Relation | Meaning |
|---|---|
| P(A ∩ B) = P(A) × P(B) | Intersection means both events occur. |
| P(H) = 1/2; P(6) = 1/6 | Heads has probability 1/2; a six has probability 1/6. |
| P(H ∩ 6) = 1/12 | One of twelve equally likely pairs qualifies. |
One worked example
- P(A ∩ B) = P(A) × P(B)Intersection means both events occur.
- P(H) = 1/2; P(6) = 1/6Heads has probability 1/2; a six has probability 1/6.
- P(H ∩ 6) = 1/12One of twelve equally likely pairs qualifies.
Watch out: Without independence this simple product is invalid. Drawing without replacement generally changes the next probability.
Goal, prerequisites and card origin
What you will learn: Find the probability that both independent events occur.
What you need first: Single-event probability and fraction multiplication.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Independence means one trial's result does not change the other's chance. Multiply probabilities when both conditions must hold.