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Two-Way Tables and Frequency Trees: Fluency and Exam Drill - Worksheets, Questions and Revision

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KS3 · Probability

KS3.M-P5D Two-Way Tables and Frequency Trees: Fluency and Exam Drill

AQA KS3.M-P5 · Calculators not allowed · about 50 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A class of 40 pupils is asked whether they prefer tea or coffee. The two-way table below shows the results.

Tea Coffee Total
Boys 9 11 20
Girls 14 6 20
Total 23 17 40

Write down the number of girls who prefer tea.
(1)
2
Using the table in Question 1, write down the total number of pupils who prefer coffee.
(1)
3
Using the table in Question 1, calculate the probability that a randomly chosen pupil prefers tea, giving your answer as a fraction in simplest form.
(1)
4
A two-way table shows whether 60 people cycle to work, split by where they live.

Cycle Do not cycle Total
Town 14 ? 40
Country 8 12 20
Total 22 38 60

Find the missing value marked '?'.
(2)
5
Using the completed table in Question 4, write down the total number of people surveyed who do not cycle to work.
(1)
6
Using the completed table in Question 4, calculate the probability that a randomly chosen person cycles to work, giving your answer as a fraction in simplest form.
(2)
7
A frequency tree shows that 80 people were asked if they play a musical instrument. 50 said yes and 30 said no. Of the 50 who play an instrument, 35 play piano and the rest play a different instrument. Write down the number who play a different instrument (not piano).
(1)
8
Using the frequency tree in Question 7, of the 30 people who do not play an instrument, 12 do drama instead. Find how many of this group do not do drama.
(2)
9
80 students are asked whether they walk to school. 45 walk and 35 do not. Of the 45 who walk, 27 live within 1 mile of school. Find the probability that a randomly chosen student walks to school AND lives within 1 mile, giving your answer as a fraction in simplest form.
(2)
10
In a frequency tree of 100 shoppers, 64 pay by card and 36 pay by cash. Of those who pay by cash, 9 are given a discount. Find the number of cash shoppers who are NOT given a discount.
(1)
11
A two-way table for 150 concertgoers shows 90 bought a programme and 60 did not. Of those who bought a programme, 54 also bought a drink. Calculate the probability that a randomly chosen concertgoer bought BOTH a programme and a drink, giving your answer as a fraction in simplest form.
(2)
12
Using the concertgoers information in Question 11, write down how many people bought a programme but NOT a drink.
(1)
13
A pet survey of 50 animals shows 32 are dogs and 18 are cats. Of the 32 dogs, 20 are male. Write down the number of female dogs.
(1)
14
A pet survey of 50 animals shows 32 dogs (of which 20 are male and 12 are female) and 18 cats (of which 8 are male and 10 are female). Calculate the total number of female pets.
(2)
15
A survey of 120 shoppers found that 70 bought fruit, 55 bought vegetables, and 25 bought both fruit and vegetables. Find the number of shoppers who bought neither fruit nor vegetables.
(3)
16
A frequency tree shows 90 students choosing a lunch option: 60 choose a hot meal and 30 choose a packed lunch. Of the 60 who choose a hot meal, 42 choose meat and the rest choose vegetarian. Of the 30 who choose a packed lunch, 12 choose a wrap and the rest choose a sandwich. Find the total number of students who chose either a vegetarian hot meal or a sandwich packed lunch.
(3)
17
In a two-way table of 200 people, 130 are employed and 70 are unemployed. Of the employed people, 91 work full-time and the rest work part-time. Calculate the probability that a randomly selected person from the 200 works part-time, giving your answer as a fraction in simplest form.
(3)
18
A two-way table shows 250 concert tickets sold: 150 for adults and 100 for children. Of the adult tickets, 96 were bought online. Of the children tickets, 40 were bought online. Find the total number of tickets bought online, and the probability that a randomly chosen ticket was bought online, as a decimal.
(3)
19
A two-way table records 300 patients at a clinic by age group and whether they received a flu vaccine this year. 180 patients are over 50, and 120 are 50 or under. Of the over-50 group, 144 received the vaccine. Of the 50-or-under group, 54 received the vaccine.
(a)Find the total number of patients who received the vaccine.(2)
(b)Find the probability that a randomly selected patient did NOT receive the vaccine, giving your answer as a fraction in simplest form.(2)
20
A school of 400 students is grouped by whether they play a sport and whether they play a musical instrument. Of the 400 students, 260 play a sport, and 90 of those who play a sport ALSO play an instrument. Overall, 150 students play an instrument.
(a)Find the number of students who play an instrument but do NOT play a sport.(1)
(b)Calculate the number of students who play NEITHER a sport NOR an instrument.(2)
(c)Calculate the probability that a randomly chosen student plays exactly one of the two activities (sport only or instrument only, not both), giving your answer as a fraction in simplest form.(1)
Mark scheme · KS3.M-P5D Two-Way Tables and Frequency Trees: Fluency and Exam Drill

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

Question 19

Question 20

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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