Venn diagrams and sets · Year 11
In Year 11 you learn: set notation.
A Venn diagram sorts things into overlapping circles inside a rectangle. The rectangle is the universal set ξ. The diagram makes it easy to count the items in one group, in both, in either or in neither. It also helps you find probabilities.
Key facts
- A ∩ B (intersection): in both A and B. This is the overlap.
- A ∪ B (union): in A or B or both.
- A′ (complement): not in A.
- Fill in a Venn diagram from the middle (the overlap) outwards.
- n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- P(A | B) = n(A ∩ B) ÷ n(B). Only look inside circle B.
Worked examples
Example 1
Using the same class, find P(F′ ∩ T) and P(F ∪ T).
Answer: 7/30 and 5/6
Example 2
The Venn diagram has 50 members. Find x, then P(B | A).
Answer: x = 10; P(B | A) = 1/3