Counting with Venn diagrams

Mathematics · Probability · ages 12-13

Name ______________________ Date ____________

On a Venn diagram, which region holds students liking both football and cricket?
- The overlap in the middle
- The left crescent only
- The right crescent only
- Outside both circles
In a Venn diagram with two circles, what do we call the region where both circles overlap?
- Union
- Intersection
- Complement
The union (A ∪ B) means things that are in A and B at the same time.
Circle one: True False
On a Venn diagram, the part outside both circles represents students who belong to:
- Both groups
- Neither group
- Group A only
In the same class, how many students like neither sport?
- 6 students
- 14 students
- 8 students
- 0 students
How many students like only cricket?
- 6 students
- 14 students
- 8 students
- 22 students
30 students: 18 like football, 14 like cricket, 8 like both. How many like only football?
- 10 students
- 18 students
- 8 students
- 2 students
What is P(a random student likes both sports)?
- 4/15
- 8/14
- 8/18
- 1/2
What is P(a random student likes football or cricket)?
- 4/5
- 3/5
- 7/15
- 1
Mia adds P(football) + P(cricket) to find P(football or cricket): 18/30 + 15/30 = 33/30. What mistake did she make?
- She counted the 8 who like both sports twice
- She used the wrong total number of students
- She should have multiplied instead of added

Answer key

For grown-ups. Fold this page away before handing over the rest.

The overlap in the middle · The overlap holds members of both sets: the intersection.
Intersection · The overlapping middle region is the intersection, written A ∩ B.
False · Union means in A, or in B, or in both. Being in both at once is the intersection, not the union.
Neither group · Anything drawn outside both circles isn't in A or B, so it stands for 'neither'.
6 students · 10 + 8 + 6 = 24 inside the circles, so 30 - 24 = 6 outside.
6 students · 14 cricket fans minus 8 in the overlap leaves 6 cricket-only.
10 students · 18 football fans minus 8 in the overlap leaves 10 football-only.
4/15 · 8 out of 30 is 8/30 = 4/15.
4/5 · 10 + 8 + 6 = 24 in the union, and 24/30 = 4/5.
She counted the 8 who like both sports twice · The 8 both-sport students sit inside each total already, so adding both totals counts them twice. Subtract P(A ∩ B) once: 33/30 minus 8/30 gives 25/30.