Conditional probability from a table
A standard method from More about probability: the steps and worked examples.
Steps
P(A | B) = (number in A and B) ÷ (number in B). The "given" part becomes the new total.
- Find the row or column of the "given" condition B. Its total is the new denominator.
- In that row or column, read the number that is also in A.
- Divide: P(A | B) = n(A ∩ B) ÷ n(B).
Worked examples
Example 1: Conditional probability from a table: 60 students were asked how they come to school.
| Bus | Walk | Total | |
|---|---|---|---|
| Late | 9 | 3 | 12 |
| On time | 21 | 27 | 48 |
| Total | 30 | 30 | 60 |
P(late | bus) = 9/30 = 3/10 "given bus": the Bus column total 30 is the new total
P(bus | late) = 9/12 = 3/4 "given late": the Late row total 12 is the new totalThe two answers differ: P(A | B) is not the same as P(B | A).
For the whole topic, read More about probability: key points, common mistakes and how the DSE tests it.