1. Venn Diagrams – Notation – Worksheet A
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4. ① A B
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5, 9, 10}
B = {3, 5, 6, 7, 10}
Complete the Venn diagram.
If I pick a number at random what is…
P(A) = 7 10
P(A AND B) = P(A ∩ B) = 3 10
P(NOT A) = P(A’) = 3 10
P(A OR B) = P(A ∪ B) = 9 10
P(B’) = = 1 2
P(A OR NOT B) = P(A ∪ B’) = = 4 5

5. A B 3 1 6 10 5 2 7 8 9 4 A’ = NOT A A ∩ B = A AND B A ∪ B = A OR B②
Remember! A B
A’ = NOT A 3 1 6 10
A ∩ B = A AND B 5 2 7
A ∪ B = A OR B 8 9 4
True or False?
P(A) = 1 2
T / F
P(A ∩ B) = 3 10
T / F
P(B) = 4 5
T / F
P(A ∪ B) = 7 10
T / F
P(A’) = 4 10
T / F
P(A ∪ B’) = 2 5
T / F

6. B F P(B ∩ F) = 15 50 = 3 10 P(B) = 25 50 = 1 2 P(F ∪ B) = 45 50 = 9 10③ B F
50 students were asked
about their lunch.
25 students had a burger (B)
35 students had fries (F)
15 students had both.
Complete the Venn diagram.
How many students had neither F or B?
If a student was chosen at random, what is…
P(B ∩ F) = = 3 10
P(B) = = 1 2
P(F ∪ B) = = 9 10
P(F) = = 7 10
P(F’ ∩ B’) = = 1 10
P(B’) = = 1 2

7. ④ ξ
100 students were asked
about their school subjects:
15 studied History (H), French (F) and Drama (D).
40 studied Drama and History.
25 studied History and French.
55 studied History.
22 studied French and Drama.
3 studied only Drama.
40 studied French.
Complete the Venn diagram with this information. H D F
P(H) = = 11 20
P(D ∩ F) = = 11 50
P(H ∪ D) = = 13 20
P(D’) = = 1 2
P(H ∩ F ∩ D) = = 3 20
P(D ∪ F) = = 16 25
P(F’) = = 3 5

9. ① A B 10 9 8 7 6 5 4 3 2 1
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5, 9, 10}
B = {3, 5, 6, 7, 10}
Complete the Venn diagram.
If I pick a number at random what is…
Answers
P(A) = 7 10
P(A AND B) = P(A ∩ B) = 3 10
P(NOT A) = P(A’) = 3 10
P(A OR B) = P(A ∪ B) = 9 10
P(B’) = = 1 2
P(A OR NOT B) = P(A ∪ B’) = = 4 5

10. A B 3 1 6 10 5 2 7 8 9 4 A’ = NOT A A ∩ B = A AND B A ∪ B = A OR B②
Remember! A B
A’ = NOT A 3 1 6 10
A ∩ B = A AND B 5 2 7
A ∪ B = A OR B 8 9 4
True or False?
P(A) = 1 2
T / F
P(A ∩ B) = 3 10
T / F
P(B) = 4 5
T / F
P(A ∪ B) = 7 10
T / F
P(A’) = 4 10
T / F
P(A ∪ B’) = 2 5
T / F

11. ③ B F
50 students were asked
about their lunch. 20 10
25 students had a burger (B)
35 students had fries (F)
15 students had both.
Complete the Venn diagram.
How many students had neither F or B?
If a student was chosen at random, what is… 15 5 5
P(B ∩ F) = = 3 10
P(B) = = 1 2
P(F ∪ B) = = 9 10
P(F) = = 7 10
P(F’ ∩ B’) = = 1 10
P(B’) = = 1 2

12. ④ ξ
100 students were asked
about their school subjects:
15 studied History (H), French (F) and Drama (D).
40 studied Drama and History.
25 studied History and French.
55 studied History.
22 studied French and Drama.
3 studied only Drama.
40 studied French.
Complete the Venn diagram with this information. H D 5 3 25 15 10 7 8 F 27
P(H) = = 11 20
P(D ∩ F) = = 11 50
P(H ∪ D) = = 13 20
P(D’) = = 1 2
P(H ∩ F ∩ D) = = 3 20
P(D ∪ F) = = 16 25
P(F’) = = 3 5

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