Venn Diagrams – Notation – Worksheet A The worksheet is in a 2 sizes.
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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’) = 5 10 = 1 2 P(A OR NOT B) = P(A ∪ B’) = 8 10 = 4 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 B ② 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
B F P(B ∩ F) = 15 50 = 3 10 P(B) = 25 50 = 1 2 P(F ∪ B) = 45 50 = 9 10 ③ 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) = 15 50 = 3 10 P(B) = 25 50 = 1 2 P(F ∪ B) = 45 50 = 9 10 P(F) = 35 50 = 7 10 P(F’ ∩ B’) = 5 50 = 1 10 P(B’) = 25 50 = 1 2
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) = 55 100 = 11 20 P(D ∩ F) = 22 100 = 11 50 P(H ∪ D) = 65 100 = 13 20 P(D’) = 50 100 = 1 2 P(H ∩ F ∩ D) = 15 100 = 3 20 P(D ∪ F) = 68 100 = 16 25 P(F’) = 60 100 = 3 5
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’) = 5 10 = 1 2 P(A OR NOT B) = P(A ∪ B’) = 8 10 = 4 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 B ② 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
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) = 15 50 = 3 10 P(B) = 25 50 = 1 2 P(F ∪ B) = 45 50 = 9 10 P(F) = 35 50 = 7 10 P(F’ ∩ B’) = 5 50 = 1 10 P(B’) = 25 50 = 1 2
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) = 55 100 = 11 20 P(D ∩ F) = 22 100 = 11 50 P(H ∪ D) = 65 100 = 13 20 P(D’) = 50 100 = 1 2 P(H ∩ F ∩ D) = 15 100 = 3 20 P(D ∪ F) = 68 100 = 16 25 P(F’) = 60 100 = 3 5
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