Using set notation to find probabilities.
14 original questions, 59 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {even numbers} B = {multiples of 5}
Kim draws a Venn diagram. She puts:
2, 4, 8 in A only 6, 10 in the intersection of A and B 5 in B only 1, 3, 9 outside both circles.
Write down two mistakes Kim has made.
A = {factors of 12} B = {factors of 18}
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 3} B = {even numbers}
Complete the Venn diagram.
40 people were asked whether they drink coffee (C) and whether they drink tea (D).
14 drink coffee only, 6 drink both, 11 drink tea only and 9 drink neither.
One of the 40 people is chosen at random.
There are 50 students in a year group.
23 study geography (G).
19 study history (H).
8 study both geography and history.
Complete the Venn diagram to show the number of students in each region.
ξ = {odd numbers between 0 and 20}
A = {multiples of 3} B = {numbers less than 10}
Draw a Venn diagram to show the sets A and B, putting every member of ξ in the correct region.
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A = {prime numbers} B = {odd numbers}
A gym has 80 members.
47 members use the treadmill (T).
39 members use the weights (W).
21 members use both the treadmill and the weights.
60 people were asked whether they have a dog (D) or a cat (C).
32 people have a dog.
27 people have a cat.
11 people have both a dog and a cat.
The Venn diagram regions for sets A and B contain these numbers of people:
A only: 7 A ∩ B: 5 B only: 8 outside both: 10
One of the people is chosen at random.
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {even numbers} B = {factors of 12}
100 people went to a music festival.
58 saw band X.
45 saw band Y.
23 saw both bands.
80 students were asked which sports they play from football (F), rugby (R) and cricket (C).
4 students play all three sports.
12 students play football and rugby.
10 students play football and cricket.
9 students play rugby and cricket.
36 students play football.
29 students play rugby.
25 students play cricket.
90 people were asked which streaming services they use from A, B and C.
5 people use all three services.
14 people use A and B.
11 people use A and C.
13 people use B and C.
40 people use A.
35 people use B.
30 people use C.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.