Sorting into Venn diagrams, two-way tables and frequency trees, set notation, and probabilities from all three.
What you will learn
- Complete a Venn diagram from totals
- Use set notation (Higher)
- Complete and use two-way tables
- Complete and use frequency trees
Fill the middle first
In a Venn diagram, each number is in exactly one region.
Start with the overlap (those in both), then subtract it from each circle's total, then work out the number outside both circles.
Totals of 30 in A and 20 in B with 8 in both give 22 in A only and 12 in B only.
If there are 50 people altogether, 22 + 8 + 12 = 42 are in a circle, so 50 − 42 = 8 are in neither. "Exactly one" means A only or B only: 22 + 12 = 34, leaving out the overlap.
For a probability from a Venn diagram, divide by everyone in the diagram, including the number outside the circles. "In A but not B" is the A-only region.
With expressions in the regions, add them all and set the total equal to the number of people: x + 3, x and 2x + 1 in the regions and 4 outside, with 40 people, give 4x + 8 = 40, so x = 8. Then put x back in to count the regions you need.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- Fill the middle first
- Set notation (Higher)
- Two-way tables
- Frequency trees
- Try it: First question
10 practice questions, marked as you go; about 25 minutes in all.
In this unit: Probability
Probabilities of single events, relative frequency, sample spaces, Venn diagrams and two-way tables, tree diagrams, and conditional probability.
- Probability basics
- Relative frequency and listing outcomes
- Venn diagrams, two-way tables and frequency trees
- Tree diagrams
- Conditional probability