Set notation and intersections.
11 original questions, 50 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A Venn diagram shows the numbers of students in a year group who take Art (A) and Music (M).
| Region | Number of students |
|---|---|
| A only | 12 |
| A ∩ M (both) | 8 |
| M only | 15 |
| Neither | 5 |
A student is chosen at random from the 40 students.
Work out P(A | M), the probability that the student takes Art given that they take Music.
100 students were asked how they travel to school. The two-way table shows the results.
| Walk | Bus | Car | Total | |
|---|---|---|---|---|
| Year 10 | 18 | 22 | 10 | 50 |
| Year 11 | 12 | 14 | 24 | 50 |
| Total | 30 | 36 | 34 | 100 |
A student is chosen at random.
Given that the student travels by bus, work out the probability that they are in Year 11.
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.
ξ = {1, 2, 3, ..., 30}
A = {multiples of 4}
B = {multiples of 6}
A number is chosen at random from ξ. Work out:
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.
100 people went to a music festival.
58 saw band X.
45 saw band Y.
23 saw both bands.
A and B are two events.
P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.7
There are 40 students in a year group.
The Venn diagram for drama (D) and music (M) shows:
D only: 10 D ∩ M: 8 M only: 12 neither: 10
Two of the students who do music are chosen at random, without replacement.
Work out the probability that both of these students also do drama.
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.