Relative and expected frequencies — Paper 2 · IGCSE Mathematics - International 0607

11 Jamil has a biased 6-sided die. He rolls it 350 times. The results are shown in the table. Number on die 1 2 3 4 5 6 Frequency 20 50 72 68 56 84 (a) Find the relative frequency of getting a 2 with Jamil’s die. … [1] (b) Explain why your answer to part (a) is a good estimate of the probability of getting a 2. … [1] (c) Estimate the number of times Jamil will get a 2 if he rolls the die 1400 times. … [1]

3 marks

Mark scheme: 11(a) 50 1 oe 350 11(b) Large sample oe 1 11(c) 200 1

This question in 0607/23 May/June 2018

4 At a railway station, the probability that any train departs on time is . 8 The number of trains in one day is 72. Work out the expected number of trains that depart on time. … [1]

1 marks

Mark scheme: 4 63 1

This question in 0607/21 Oct/Nov 2019

8 200 students record the method they use most to travel to school. The results are shown in the table. Method of travel Bus Car Walk Cycle Number of students 40 98 37 25 (a) Find, as a fraction, the relative frequency of a student travelling to school by bus. … [1] (b) Give a reason why it is reasonable to use your answer to part (a) to estimate the probability that a student travels to school by bus. … [1] (c) The school has 1800 students. Estimate the number of students who travel to school by bus. … [1]

3 marks

Mark scheme: 8(a) 40 1 oe 200 8(b) Large sample oe 1 8(c) 360 1 FT for their (a) × 1800

This question in 0607/23 Oct/Nov 2019

6 A biased four-sided spinner is spun 150 times. The number of times that the spinner lands on each number is shown in the table. Number on spinner 1 2 3 4 Frequency 34 63 27 26 (a) Write down the relative frequency of the spinner landing on 2. … [1] (b) Explain why it is reasonable to use your answer to part (a) as the probability of this spinner landing on 2. … [1] (c) The spinner is spun 3000 times. Find the expected number of times that the spinner lands on 2. … [2]

4 marks

Mark scheme: 6(a) 63 1 oe 150 6(b) Large sample oe 1 6(c) 1260 2 63 M1 for their × 3000 oe 150

This question in 0607/23 May/June 2020

9 Pierre records the colour of each of 200 cars passing his home. The table shows the results. Colour Silver Black Red Green Blue Other Frequency 23 68 35 20 32 22 (a) Write down the relative frequency of a silver car. … [1] (b) Explain why it is reasonable to use the answer to part (a) as the probability that the next car which passes will be silver. … [1] (c) Over the whole day 1200 vehicles pass Pierre’s home. Estimate the number of these cars that are silver. … [1]

3 marks

Mark scheme: 9(a) 23 1 or 0.115 200 9(b) Large sample oe 1 9(c) 138 1

This question in 0607/22 Oct/Nov 2020

7 Mia carries out a survey in a school to find out what students will do when they leave school. These are her results. University Job Training Travelling Total Frequency 112 43 27 18 200 (a) Find the relative frequency of university. … [1] (b) There are 1600 students in this school. (i) Explain why the result in part (a) is a reasonable estimate of the probability that a student from this school will go to university. … [1] (ii) Calculate an estimate for the number of students in this school who will go travelling. … [2]

4 marks

Mark scheme: 7(a) 112 1 oe 200 7(b)(i) Large sample 1 7(b)(ii) 144 2 18 M1 for × 1600 oe 200

This question in 0607/21 Oct/Nov 2021

5 There are 640 students in a school. The table shows the favourite colour of each of the students. Favourite colour Blue Green Red Yellow Number of students 120 2x 280 x (a) Find the value of x. x = … [2] (b) Find the relative frequency of students whose favourite colour is red. Give your answer as a fraction in its lowest terms. … [2]

4 marks

Mark scheme: 5(a) 80 2 M1 for (640 − 120 − 280) ÷ (2 + 1) 5(b) 7 2 280 cao M1 for oe 16 640

This question in 0607/23 Oct/Nov 2021

7 Eggs are graded into four sizes: extra large, large, medium and small. A farmer records the sizes of a sample of 100 eggs that she collects. The results are shown in the table. Size Extra large Large Medium Small Number of eggs 28 36 24 12 (a) Find the relative frequency for large eggs. … [1] (b) In one month, the farmer collects 2500 eggs. Calculate an estimate for the number of these eggs that are small. … [2]

3 marks

Mark scheme: 7(a) 36 9 1 or oe 100 25 7(b) 300 2 2500 M1 for 12  oe 100

This question in 0607/23 May/June 2022

5 A biased 5-sided spinner is spun 200 times. The results are shown in the table. Number 1 2 3 4 5 Frequency 24 48 63 38 27 (a) Find the relative frequency of the spinner landing on 2. … [1] (b) The spinner is spun 1000 times. Find the expected number of times that the spinner lands on 2. … [1]

2 marks

Mark scheme: 5(a) 48 1 oe 200 5(b) 240 1

This question in 0607/22 Oct/Nov 2022

8 Salma spins a biased spinner with sectors labelled 1, 2, 3, 4 and 5. The table shows the relative frequencies of each of her scores. Score 1 2 3 4 5 Relative frequency 0.1 0.05 0.3 0.35 p (a) Find the value of p. … [2] (b) Salma spins the spinner 4000 times. Work out an estimate for the number of times she scores 3. … [1]

3 marks

Mark scheme: 8(a) 0.2 oe 2 M1 for 1 – (0.1 + 0.05 + 0.3 + 0.35) or B1 for 0.8 seen 8(b) 1200 1

This question in 0607/22 May/June 2023

5 One day Hassan surveys the number of people in the cars passing his house. The results for the first 100 cars are shown in the table. Number of people 1 2 3 4 5 6 Frequency 42 23 17 9 7 2 Relative frequency (a) Complete the table. [2] (b) A total of 1200 cars pass Hassan’s house that day. Calculate an estimate of the number of these cars with 5 people. … [1]

3 marks

Mark scheme: 5(a) 0.42, 0.23, 0.17, 0.09, 0.07, 0.02 oe 2 B1 for 3 or more correct. 5(b) 84 1

This question in 0607/23 Oct/Nov 2023

7 Shami asked 200 people from a town about their favourite type of TV programme. These are the results. Type of Sport Comedy Drama Quiz Reality Documentary programme Frequency 46 38 23 21 56 16 (a) Find the relative frequency of Reality. … [1] (b) The town has 40 000 inhabitants. Work out the expected number of people in the town whose favourite type of programme is Documentary. … [2]

3 marks

Mark scheme: 7(a) 56 1 oe 200 7(b) 3200 2 16 M1 for [40000 ]200

This question in 0607/22 Feb/March 2024

10 The table shows the favourite colour of each of 80 people. Colour Red Blue White Green Silver Black Yellow Frequency 23 17 11 9 12 3 x (a) Find the value of x. … [1] (b) Find the relative frequency of silver, giving your answer as a fraction in its lowest terms. … [2]

3 marks

Mark scheme: 10(a) 5 1 10(b) 3 2 12 cao B1 for oe 20 80

This question in 0607/21 May/June 2024

6 The types of vehicle travelling on a road were recorded. The table shows the results for a sample of 200 vehicles. Type of vehicle Car Van Truck Motorcycle Number of vehicles 84 64 40 12 Relative frequency (a) Complete the table. [2] (b) One day 5000 vehicles use the road. Work out an estimate for the number of trucks that use the road that day. … [1]

3 marks

Mark scheme: 6(a) 84 64 40 12 2 B1 for 2 correct. oe 200 200 200 200 6(b) 1000 1

This question in 0607/21 Oct/Nov 2025