M4.6.6 For the adult
Venn diagrams and sets
In a class of 30, 17 like football, 12 like running, and 5 like both. What is the chance that a pupil chosen at random likes football or running?
What this chapter teaches
A Venn diagram puts two sets in a box. Start with the overlap, then take it off each total. The four regions add to the whole. P(A or B) = P(A) + P(B) − P(A and B), written P(A ∪ B) and P(A ∩ B) in set notation.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do you start with the overlap when you fill in a Venn diagram?
- Why must you take away P(A and B) when you find P(A or B)?
- What does A′ mean, and how do you find its chance?
After the chapter, the learner can
- Draw a Venn diagram for two sets
- Find P(A or B) and P(A and B) from a Venn diagram
- Use set notation like A ∪ B and A ∩ B
What they copy into their notebook
Start with the overlap. Regions add to the whole. A ∩ B is both. A ∪ B is either or both. P(A ∪ B) = P(A) + P(B) − P(A ∩ B). P(A′) = 1 − P(A).