Success Homeschool

Year 9 Mathematics · Venn diagrams and two-way tables

Name: ______________________

Date: ____________

1. In a group of 50 people, 28 like cats, 20 like dogs and 8 like both. How many like cats only?
- ☐ (a) 28
- ☐ (b) 20
- ☐ (c) 8
- ☐ (d) 12
2. In the same group of 50 (28 like cats, 20 like dogs, 8 like both), how many like neither?
- ☐ (a) 10
- ☐ (b) 2
- ☐ (c) 18
- ☐ (d) 22
3. In the same group, what is the probability that a person chosen at random likes both cats and dogs?
- ☐ (a) 425
- ☐ (b) 848
- ☐ (c) 18
- ☐ (d) 25
4. In a Venn diagram, the event “A or B” means:
- ☐ (a) only the overlap
- ☐ (b) everything inside A, B or both
- ☐ (c) everything outside both circles
- ☐ (d) A but not B
5. In the same group of 50 (28 like cats, 20 like dogs, 8 like both), find P(likes cats or dogs) as a fraction in simplest form.
6. In the same group of 50, find P(does not like dogs) as a fraction in simplest form.
7. A two-way table of 60 students shows: owns a bike and has a pet 18; owns a bike, no pet 12; no bike, has a pet 22; no bike, no pet 8. Find P(owns a bike and has a pet) as a fraction in simplest form.
8. Using the same table of 60 students, find P(owns a bike or has a pet) as a fraction in simplest form.

Answer sheet

1. 20 — Cats only = 28 − 8 = 20.
2. 10 — Cats only 20 + both 8 + dogs only 12 = 40 inside the circles, so 50 − 40 = 10 like neither.
3. 425 — 8 of the 50 people like both: 850 = 425.
4. everything inside A, B or both — “Or” includes A only, B only and the overlap.
5. 4/5 — 40 people are inside the circles: 4050 = 45.
6. 3/5 — 50 − 20 = 30 people do not like dogs: 3050 = 35.
7. 3/10 — 1860 = 310.
8. 13/15 — Count each cell once: 18 + 12 + 22 = 52. 5260 = 1315. (Only the 8 with no bike and no pet are left out.)