Conditional probability is the chance of A when we already know B has happened, written P(A | B). Knowing B shrinks the set of possible outcomes to just B.
If 20 students study subjects and 16 study history, 5 study geography and 3 study both, then P(geography | history) = 3/16: of the 16 history students, 3 also study geography. The formula is P(A | B) = P(A and B) ÷ P(B). Two-way tables and Venn diagrams make these easy to read.
Worked example
Cards 1 to 20. A card is even. What is the probability it is a multiple of 3?
- Even cards: 10 of them.
- Even multiples of 3: 6, 12, 18, which is 3.
Answer:3/10
Key words
- conditional probability
- probability given that something is known
- given that
- the condition
- P(A | B)
- probability of A given B
Practise this
New questions every time.
Common Core-referenced: HSS-CP.A.3, HSS-CP.B.6