PEAZIT Aha card
Go straight to resources ↓A condition narrows the group you select from
Knowing B holds, measure the chance of A only among B cases. The denominator describes this restricted group, not all original cases.
| Relation | Meaning |
|---|---|
| P(A|B) = P(A ∩ B)/P(B) | Divide by the conditioning probability; P(B) must be positive. |
| |B| = 8; |A ∩ B| = 3 | The new group is the eight club members. |
| P(A|B) = 3/8 | Three of eight satisfy the second condition. |
One worked example
- P(A|B) = P(A ∩ B)/P(B)Divide by the conditioning probability; P(B) must be positive.
- |B| = 8; |A ∩ B| = 3The new group is the eight club members.
- P(A|B) = 3/8Three of eight satisfy the second condition.
Watch out: Counting assumes uniform random selection within the given group. Conditional probabilities generally cannot be reversed.
Goal, prerequisites and card origin
What you will learn: Calculate probability after gaining additional information.
What you need first: Equally likely outcomes and fractions.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Knowing B holds, measure the chance of A only among B cases. The denominator describes this restricted group, not all original cases.