Priya asked 60 people whether they prefer tea or coffee. 37 of them said they prefer tea. The frequency tree below shows this information.
(a)Complete the frequency tree by working out the number of people who prefer coffee.(2)
(b)One of the 60 people is chosen at random. Write down the probability that this person prefers coffee. Give your answer as a fraction.(1)
(Total for Question 1 is 3 marks)
2
Dwayne asked 45 pupils whether they own a pet. 26 of them said yes.
(a)Complete the frequency tree by working out the number of pupils who do not own a pet.(2)
(b)A pupil is chosen at random from the 45 pupils. Work out the probability that this pupil owns a pet. Give your answer as a decimal, correct to 2 decimal places.(2)
(Total for Question 2 is 4 marks)
3
At a gym, 50 members were asked whether they are under 18 or 18 and over, and whether they attend morning or evening classes. 20 members are under 18. Of the under-18 members, 14 attend morning classes. Of the members who are 18 and over, 12 attend morning classes.
(a)Complete the frequency tree by working out the two missing numbers of members who attend evening classes.(2)
(b)Work out the total number of members who attend evening classes.(1)
(Total for Question 3 is 3 marks)
4
A youth club has 84 members. 3/4 of the members have at least one sibling.
(a)Show that the number of members with at least one sibling is 63.(2)
(b)Hence work out the number of members with no siblings.(1)
(c)Of the members with at least one sibling, 2/9 have 3 or more siblings. Work out the number of members who have 3 or more siblings.(2)
(Total for Question 4 is 5 marks)
5
A survey asked 150 adults whether they exercise regularly. 60% of the adults said yes.
(a)Work out the number of adults who exercise regularly.(2)
(b)Of the adults who exercise regularly, 30% also go to a gym. Work out the number of adults who go to a gym.(2)
(c)Work out the number of adults who do not exercise regularly.(1)
(Total for Question 5 is 5 marks)
6
There are 96 students in Year 11. They study triple science or combined science in the ratio 5 : 3.
(a)Work out the number of students who study triple science.(2)
(b)Work out the number of students who study combined science.(1)
(c)Of the triple science students, 1/4 achieved a grade 9. Work out the number of triple science students who achieved a grade 9.(2)
(Total for Question 6 is 5 marks)
7
A cafe manager recorded whether 120 customers bought a hot or a cold drink, and whether they also bought a snack. The completed frequency tree is shown below.
(a)Write down the number of customers who bought a cold drink and a snack.(1)
(b)One customer is chosen at random from the 120 customers. Work out the probability that this customer bought a hot drink and did not buy a snack. Give your answer as a fraction in its simplest form.(2)
(c)Work out the total number of customers who bought a snack.(1)
(Total for Question 7 is 4 marks)
8
A student has started a frequency tree to show whether 80 pupils have school dinners or a packed lunch, and whether they are vegetarian. The tree states: Total = 80; School dinners = 45, of which Vegetarian = 20 and Non-vegetarian = 30.
(a)Explain why the frequency tree cannot be correct.(1)
(b)The number of non-vegetarian pupils having school dinners, 30, is correct. Work out the correct number of vegetarian pupils having school dinners.(1)
(Total for Question 8 is 2 marks)
9
A survey of 80 pupils, 40 in Year 10 and 40 in Year 11, recorded whether they walk to school. 18 of the Year 10 pupils walk to school. 25 of the Year 11 pupils walk to school.
(a)Work out the number of Year 10 pupils who do not walk to school.(1)
(b)Work out the number of Year 11 pupils who do not walk to school.(1)
(c)One pupil is chosen at random from all 80 pupils. Work out the probability that this pupil walks to school. Give your answer as a fraction in its simplest form.(2)
(Total for Question 9 is 4 marks)
10
A survey of 120 sports fans recorded which team they support and how they watched the last match. The completed frequency tree is shown below: Total = 120; Team A = 75 (Live = 45, TV = 30); Team B = 45 (Live = 20, TV = 25). Show that the total number of fans who watched the match on TV is 55.
(Total for Question 10 is 2 marks)
11
64 students were asked whether they are going on the school trip. 45 of them said yes.
(a)Complete the frequency tree by working out the number of students who are not going on the trip.(1)
(b)Of the students going on the trip, 3 in every 5 need a packed lunch from school. Work out how many students need a packed lunch.(2)
(c)Each packed lunch costs 3.50 pounds. Work out the total cost of all the packed lunches needed.(2)
(Total for Question 11 is 5 marks)
12
Leah surveyed 90 people to find out whether they recycle plastic. 63 of them said yes.
(a)Complete the frequency tree by working out the number of people who do not recycle plastic.(1)
(b)Of the people who recycle plastic, 5/9 also recycle glass. Work out the number of people who recycle both plastic and glass.(2)
(c)One person is chosen at random from all 90 people. Work out the probability that this person recycles plastic but not glass. Give your answer as a fraction in its simplest form.(2)
(Total for Question 12 is 5 marks)
13
72 pupils were asked their eye colour and whether they are left-handed or right-handed. 48 pupils have brown eyes. Of the brown-eyed pupils, 40 are right-handed. Of the blue-eyed pupils, 21 are right-handed.
(a)Complete the frequency tree by working out the number of pupils with blue eyes.(1)
(b)Work out the total number of pupils who are left-handed.(2)
(c)A pupil is chosen at random. Work out the probability that this pupil has brown eyes and is right-handed. Give your answer as a decimal, correct to 3 significant figures.(2)
(Total for Question 13 is 5 marks)
14
An ice cream van recorded whether 150 customers chose vanilla or chocolate, and whether they added a topping. 90 customers chose vanilla, of whom 54 added a topping. Of the customers who chose chocolate, 42 added a topping.
(a)Work out the number of customers who chose chocolate.(1)
(b)Work out the number of chocolate customers who did not add a topping.(1)
(c)A topping costs an extra 0.60 pounds. Work out the total extra money made from all the toppings sold.(2)
(Total for Question 14 is 4 marks)
15
96 gym members were asked whether they prefer cardio or weights, and whether they use classes. 60 members prefer cardio, of whom 45 use classes. Of the members who prefer weights, 9 use classes.
(a)Write the number of cardio members who use classes as a fraction of all cardio members. Give your answer in its simplest form.(2)
(b)Work out the total number of members (cardio and weights) who use classes.(1)
(c)Work out the probability that a randomly chosen member prefers weights and does not use classes. Give your answer as a fraction in its simplest form.(2)
(Total for Question 15 is 5 marks)
16
A charity bake sale sold 45 cakes. 27 of the cakes were sold to adults. Of the cakes sold to adults, 1/3 were gluten-free. Of the cakes sold to children, 2/9 were gluten-free.
(a)Work out the number of cakes sold to children.(1)
(b)Work out the number of gluten-free cakes sold to adults.(2)
(c)Given that 4 of the cakes sold to children were gluten-free, work out the total number of gluten-free cakes sold.(1)
(Total for Question 16 is 4 marks)
17
A researcher randomly surveyed 40 residents of a town about car ownership. 24 of the residents have a car. Of the residents with a car, 9 have an electric car.
(a)Complete the frequency tree by working out the number of residents in the sample with no car, and the number with a car that is not electric.(2)
(b)The town has 8000 residents. Use the survey to estimate the number of residents in the town who have an electric car.(2)
(Total for Question 17 is 4 marks)
18
200 people were asked how they travel to work. The frequency tree shows the number who travel by bus as x, and the number who do not travel by bus as (x + 40).
(a)Form and solve an equation to find the value of x.(3)
(b)Write down the number of people who do not travel by bus.(1)
(Total for Question 18 is 4 marks)
19
School A has 200 students, of whom 120 study a language. School B has 150 students, of whom 84 study a language.
(a)Work out the percentage of School A students who study a language.(2)
(b)Work out the percentage of School B students who study a language.(2)
(c)State, with a reason, which school has the greater proportion of students studying a language.(1)
(Total for Question 19 is 5 marks)
20
A charity fair was attended by 280 people. 5/8 of them paid to enter the raffle. Of the raffle entrants, 20% won a prize. Of the people who did not enter the raffle, 1/3 bought refreshments.
(a)Work out the number of people who paid to enter the raffle.(2)
(b)Work out the number of people who did not enter the raffle.(1)
(c)Of the raffle entrants, 20% won a prize. Work out the number of raffle entrants who won a prize.(2)
(d)Show that the total number of people who did not win a prize (including those who did not enter the raffle) is 245.(2)
(Total for Question 20 is 7 marks)
Mark scheme · 3.19 Frequency Trees
Question 1
(a) M1 60 - 37
(a) A1 23 cao
(a) Answer: 23
(b) B1ft 23/60 oe (follow through from part a)
(b) Answer: 23/60
Question 2
(a) M1 45 - 26
(a) A1 19 cao
(a) Answer: 19
(b) M1 26 / 45
(b) A1 awrt 0.58
(b) Answer: 0.58
Question 3
(a) B1 6 (20 - 14) for under-18 evening
(a) B1 18 (30 - 12) for 18-and-over evening
(a) Answer: 6 and 18
(b) B1ft 24 (6 + 18), follow through from part a
(b) Answer: 24
Question 4
(a) M1 84 x 3/4
(a) A1 = 63 cso (method and answer 63 must both be shown)
(a) Answer: 63
(b) B1ft 21 (84 - 63)
(b) Answer: 21
(c) M1 63 x 2/9
(c) A1 14 oe
(c) Answer: 14
Question 5
(a) M1 150 x 0.6
(a) A1 90 cao
(a) Answer: 90
(b) M1ft 90 x 0.3
(b) A1ft 27
(b) Answer: 27
(c) B1ft 60 (150 - 90)
(c) Answer: 60
Question 6
(a) M1 96 / 8 (= 12), oe
(a) A1 60 (12 x 5) cao
(a) Answer: 60
(b) B1ft 36 (12 x 3 or 96 - 60)
(b) Answer: 36
(c) M1ft 60 / 4
(c) A1ft 15
(c) Answer: 15
Question 7
(a) B1 15 cao
(a) Answer: 15
(b) M1 28/120
(b) A1 7/30 oe
(b) Answer: 7/30
(c) B1 57 (42 + 15)
(c) Answer: 57
Question 8
(a) B1 20 + 30 = 50, which is not equal to 45 oe
(a) Answer: 20 + 30 = 50, not 45, so the branches do not add up to the school dinners total
(b) B1ft 15 (45 - 30)
(b) Answer: 15
Question 9
(a) B1 22 (40 - 18)
(a) Answer: 22
(b) B1 15 (40 - 25)
(b) Answer: 15
(c) M1 (18 + 25)/80
(c) A1 43/80 oe (does not simplify further)
(c) Answer: 43/80
Question 10
M1 30 + 25
A1 = 55 cso (both figures 30 and 25 must be identified from the tree)
Answer: 55
Question 11
(a) B1 19 (64 - 45)
(a) Answer: 19
(b) M1 45 x 3/5
(b) A1 27 cao
(b) Answer: 27
(c) M1ft 27 x 3.50
(c) A1ft 94.50 (pounds), oe with correct units
(c) Answer: GBP 94.50
Question 12
(a) B1 27 (90 - 63)
(a) Answer: 27
(b) M1 63 x 5/9
(b) A1 35 cao
(b) Answer: 35
(c) M1ft (63 - 35)/90
(c) A1ft 14/45 oe
(c) Answer: 14/45
Question 13
(a) B1 24 (72 - 48)
(a) Answer: 24
(b) M1 (48 - 40) + (24 - 21)
(b) A1 11 cao
(b) Answer: 11
(c) M1 40/72
(c) A1 awrt 0.556
(c) Answer: 0.556
Question 14
(a) B1 60 (150 - 90)
(a) Answer: 60
(b) B1ft 18 (60 - 42)
(b) Answer: 18
(c) M1 (54 + 42) x 0.60
(c) A1 57.60 (pounds), oe with correct units
(c) Answer: GBP 57.60
Question 15
(a) M1 45/60
(a) A1 3/4 oe
(a) Answer: 3/4
(b) B1 54 (45 + 9)
(b) Answer: 54
(c) M1 27/96, where weights = 96 - 60 = 36 and no classes = 36 - 9 = 27