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Two Way Tables - Worksheets, Questions and Revision

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GCSE · Statistics: representing and interpreting data

3.20 Two Way Tables

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Miss Wallace surveyed the pupils in Year 7 and Year 8 about how they travel to school. Some of the results are shown in the two-way table below.
Method of travel to school Walk Cycle Total Year 7 Year 8 Total 9 6 9 35
(a)Complete the two-way table.(5)
(b)Write down the number of Year 8 pupils who cycle to school.(1)
(c)One pupil is chosen at random from Year 8. Find the probability that this pupil walks to school.(2)
(Total for Question 1 is 8 marks)
2
Mrs Ahmed recorded the lunch choices of 60 pupils in the school canteen. The two-way table shows some of the results.
Sandwich Hot meal Total Year 9 Year 10 Total 14 16 30 10 20 30 36 60
(a)Write down the number of Year 10 students who chose a hot meal.(1)
(b)Work out the total number of students who chose a sandwich.(2)
(Total for Question 2 is 3 marks)
3
Mr Nkemelu asked 90 students in Year 10 and Year 11 to name their favourite subject from Maths, English and Science. The completed two-way table shows the results.
Favourite Subject Maths English Science Total Year 10 Year 11 Total 18 14 8 40 12 20 18 50 30 34 26 90
(Total for Question 3 is 2 marks)
4
Priya Chandra manages Riverside Car Park. She recorded how many cars and vans were parked there in the morning and in the afternoon.
Vehicles at Riverside Car Park Morning Afternoon Total Cars Vans Total 45 25 60 120
(Total for Question 4 is 5 marks)
5
The completed two-way table from Priya's car park survey is shown below.
Morning Afternoon Total Cars Vans Total 45 35 80 15 25 40 60 60 120
(Total for Question 5 is 2 marks)
6
Mr Choudhury owns a corner shop. He recorded how 200 customers paid for their shopping, and whether they shopped in the morning or the evening. The completed two-way table is shown below.
Morning Evening Total Card Cash Total 60 70 130 40 30 70 100 100 200
(a)Write down the total number of customers who shopped in the morning.(1)
(b)Work out the percentage of all 200 customers who paid by cash.(2)
(c)A customer who shopped in the evening is chosen at random. Work out the probability that they paid by card.(2)
(Total for Question 6 is 5 marks)
7
Ms Bianchi, a form tutor, asked 50 students whether they prefer Maths or English. 28 of the students are boys. Of the boys, 12 prefer Maths. Of the girls, 18 prefer English.
(a)Draw and complete a two-way table to show this information.(5)
(b)Write down the number of girls who prefer Maths.(1)
(c)One student is chosen at random from the 50 students. Find the probability that this student prefers Maths.(2)
(Total for Question 7 is 8 marks)
8
Chloe Bennett, a council officer, surveyed 80 households about whether they recycle glass and whether they recycle paper. The completed two-way table is shown below.
Recycles Paper Yes No Total Recycles Glass Yes No Total 42 8 50 18 12 30 60 20 80
(a)Write down the number of households that recycle neither glass nor paper.(1)
(b)Find the probability that a randomly chosen household recycles both glass and paper.(2)
(c)One household is chosen at random from those that recycle paper. Find the probability that this household does not recycle glass.(2)
(Total for Question 8 is 5 marks)
9
Tomasz Nowak runs an ice cream stall at a fair. He recorded which flavour was bought by 100 customers, split by Adult and Child. The completed two-way table is shown below.
Vanilla Chocolate Strawberry Total Adult Child Total 15 25 10 50 20 18 12 50 35 43 22 100
(a)Which flavour was the most popular overall?(1)
  • A) Vanilla
  • B) Chocolate
  • C) Strawberry
  • D) Cannot be determined
(b)Work out the probability that a randomly selected customer chose strawberry.(2)
(Total for Question 9 is 3 marks)
10
Freya Sinclair organised a charity bake sale where 90 cakes were sold, either Sponge or Chocolate, in the morning or the afternoon. Some of the results are shown in the two-way table below.
Cakes sold at bake sale Sponge Chocolate Total Morning Afternoon Total 22 48 52 90
(Total for Question 10 is 5 marks)
11
Mrs Osei, the school nurse, recorded whether pupils in Class A and Class B have a peanut allergy, out of 60 pupils in total. The completed two-way table is shown below.
Peanut Allergy Allergy Yes Allergy No Total Class A Class B Total 4 26 30 6 24 30 10 50 60
(a)Write down the number of pupils in Class B who do not have a peanut allergy.(1)
(b)Work out the probability that a randomly selected pupil (from all 60) has a peanut allergy.(2)
(c)One pupil is chosen at random from Class A. Find the probability that this pupil does not have a peanut allergy.(2)
(Total for Question 11 is 5 marks)
12
Mr Fitzgerald recorded the exam results of 100 students who each sat one exam, either Maths or Science. The completed two-way table is shown below.
Pass Fail Total Maths Science Total 38 12 50 33 17 50 71 29 100
(a)Write down the total number of students who failed their exam.(1)
(b)A student says that a greater proportion of Maths students passed than Science students. Determine, showing your working, whether the student is correct.(3)
(Total for Question 12 is 4 marks)
13
Aisha Malik surveyed a sample of 60 visitors to a museum about whether they bought a souvenir, split by Adult and Child. The completed two-way table is shown below.
Bought souvenir Did not buy Total Adult Child Total 9 21 30 15 15 30 24 36 60
(a)Find the probability that a randomly chosen visitor from the sample bought a souvenir.(2)
(b)There are 900 visitors to the museum on Saturday. Use the table to estimate the number of these visitors who will buy a souvenir.(3)
(Total for Question 13 is 5 marks)
14
Marcus Reid coaches a running club with 40 members. The completed two-way table shows how many members finished a marathon, split by gender.
Finished Did not finish Total Male Female Total 20 10 30 5 5 10 25 15 40
(a)Write down the number of female members who finished the marathon.(1)
(b)Find the probability that a randomly chosen member did not finish the marathon.(2)
(c)20% of the members who did not finish the marathon were injured during the race. Work out how many members did not finish due to injury.(2)
(Total for Question 14 is 5 marks)
15
Mrs Devine, an assistant head teacher, checked whether 90 pupils across three tutor groups had completed their homework. The completed two-way table is shown below.
7A 7B 7C Total Completed 24 18 28 70 Not done 6 12 2 20 Total 30 30 30 90
(a)Write down the number of pupils in 7B who had not completed their homework.(1)
(b)Find the probability that a randomly chosen pupil (from all 90) had completed their homework.(2)
(c)One pupil is chosen at random from 7C. Find the probability that this pupil had completed their homework.(2)
(Total for Question 15 is 5 marks)
16
Ade Okafor surveyed 120 adults about whether they prefer to read a Tabloid or a Broadsheet newspaper. The number of males who prefer a Tabloid is 2x, and the number of females who prefer a Tabloid is (x + 10). 28 males prefer a Broadsheet, and 37 females prefer a Broadsheet.
Tabloid Broadsheet Total Male Female Total 2x 28 (x + 10) 37 120
(a)Form and solve an equation to find the value of x.(3)
(b)Work out the total number of male adults in the survey.(2)
(Total for Question 16 is 5 marks)
17
Kwame Mensah manages a leisure centre with 120 members. The completed two-way table shows the age and gender of the members.
Under 30 30 and over Total Male Female Total 34 26 60 28 32 60 62 58 120
(a)Write down the number of female members aged 30 and over.(1)
(b)One member under 30 is chosen at random. Show that the probability this member is male is 17/31.(2)
(Total for Question 17 is 3 marks)
18
Grace Adeyemi is a quality control supervisor at a factory. 300 items were tested for faults using two machines, A and B. Machine A tested 3/5 of all 300 items, and Machine B tested the rest. Of the items tested by Machine A, 1 in 20 were found to be faulty. Of the items tested by Machine B, 15% were found to be faulty.
(a)Work out the number of items tested by Machine A and the number of items tested by Machine B.(3)
(b)Complete a two-way table to show the number of faulty and non-faulty items for each machine.(4)
(c)Work out the total number of faulty items out of the 300 tested.(2)
(Total for Question 18 is 9 marks)
Mark scheme · 3.20 Two Way Tables

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

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Question 1

8 marks
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Question 2

3 marks
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Question 3

2 marks

Question 4

5 marks
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Question 5

2 marks

Question 6

5 marks
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Question 7

8 marks
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Question 8

5 marks
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Question 9

3 marks
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Question 10

5 marks
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Question 11

5 marks
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Question 12

4 marks
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Question 13

5 marks
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Question 14

5 marks
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Question 15

5 marks
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Question 16

5 marks
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Question 17

3 marks
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Question 18

9 marks
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