Relative and expected frequencies — Paper 1 · IGCSE Mathematics 0580

4 2 When Ali takes a penalty, the probability that he will score a goal is . 5 Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer [2]

2 marks

Mark scheme: 4 2 24 or 24 out of 30 2 M1 for × 30 5

This question in 0580/11 Oct/Nov 2011

14 Ying spins a spinner 75 times. The table shows her results. Yellow Green Red Blue Colour Red Blue Green Yellow Frequency 17 24 20 14 (a) Write down the relative frequency of the spinner stopping on blue. Answer(a) [1] (b) Tony spins the same spinner 450 times. Find the expected number of times the spinner stops on yellow. Answer(b) [2]

3 marks

Mark scheme: 24 14 (a) oe 1 75 14 (b) 84 2 M1 for 450× or 6 × 14 75 IGCSE – October/November 2012 0580 11 20 ( ) 360 [ 160] 1

This question in 0580/11 Oct/Nov 2012

12 The probability of Sachin’s team winning any match is 0.45. (a) Write down the probability of Sachin’s team not winning any match. Answer(a) … [1] (b) In a season there are 40 matches. How many matches should Sachin’s team expect to win in a season? Answer(b) … [2] _____________________________________________________________________________________

3 marks

Mark scheme: 12 (a) [0].55 oe 1 (b) 18 2 M1 for 40 × [0].45 oe IGCSE – May/June 2013 0580 11

This question in 0580/11 May/June 2013

14 S P A C E S One of the 6 letters is taken at random. (a) Write down the probability that the letter is S. Answer(a) … [1] (b) The letter is replaced and again a letter is taken at random. This is repeated 600 times. How many times would you expect the letter to be S? Answer(b) … [1] _____________________________________________________________________________________

2 marks

Mark scheme: 2 14 (a) oe 1 6 (b) 200 Final answer 1FT FT 600 × their (a) providing their (a) is a probability

This question in 0580/11 Oct/Nov 2013

3 Zingon make light bulbs. 1 The probability that a Zingon light bulb is faulty is . 20 Gina tests 240 of these light bulbs. How many of them would she expect to be faulty? Answer … [1] _____________________________________________________________________________________

1 marks

Mark scheme: 3 12 final answer 1

This question in 0580/12 Oct/Nov 2013

16 A bag contains different coloured counters. Sasha takes a counter at random, records its colour, and replaces it. She does this 90 times and records her results in the pie chart below. Green Red 136° 148° Blue (a) Write down the relative frequency of Sasha choosing a red counter. Answer(a) … [1] (b) Work out the number of times a green counter is chosen. Answer(b) … [3] __________________________________________________________________________________________

4 marks

Mark scheme: 16 (a) 136 1 oe 360 (b) 19 cao 3 B1 for 76 their 76 M1 for × 90 360

This question in 0580/12 Oct/Nov 2014

7 The probability that Raju arrives on time at school is 0.72 . (a) Write down the probability that he will not arrive on time. Answer(a) … [1] (b) Raju attends school on 200 days. Work out the expected number of days he will arrive on time. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 7 (a) 0.28 oe 1 (b) 144 1

This question in 0580/12 Feb/March 2015

9 Dan either walks or cycles to school. The probability that he cycles to school is 13 . (a) Write down the probability that Dan walks to school. … [1] (b) There are 198 days in a school year. Work out the expected number of days that Dan cycles to school in a school year. … [1]

2 marks

Mark scheme: 2 9 (a) oe 1 3 (b) 66 cao 1 11 11

This question in 0580/12 Feb/March 2016

15 Cups are made in a factory. The probability that one of these cups is faulty is 0.02 . (a) Find the probability that a cup is not faulty. … [1] (b) In one day 2500 cups are made. Work out the number of these cups that are expected to be faulty. … [2]

3 marks

Mark scheme: 15 (a) 0.98 oe 1 (b) 50 cao 2 M1 for 2500 × 0.02 If zero scored, SC1 for answer of 2450

This question in 0580/12 Oct/Nov 2016

15 Maria asks 50 students in her school when their birthday is. She records the information in the table. Jan to Mar Apr to Jun Jul to Sep Oct to Dec Number of birthdays 9 21 14 6 (a) Find the relative frequency of a student having a birthday in April, May or June. … [1] (b) There are 750 students in the school. Estimate the number of students who have a birthday in April, May or June. … [1]

2 marks

Mark scheme: 15(a) 21 1 oe 50 15(b) 315 1FT FT their (a) × 750 provided 0 < their (a) < 1

This question in 0580/11 May/June 2017

17 (a) A box contains 3 blue pens, 4 red pens and 8 green pens only. A pen is chosen at random from the box. Find the probability that this pen is green. … [1] (b) A cube has only one of its six faces painted yellow. This cube is rolled 240 times. Work out the expected number of times that it lands on the yellow face. … [1]

2 marks

Mark scheme: 17(a) 8 1 oe 15 17(b) 40 1

This question in 0580/11 May/June 2018

18 The probability that a sweet made in a factory is the wrong shape is 0.0028 . One day, the factory makes 25 000 sweets. Calculate the number of sweets that are expected to be the wrong shape. … [2]

2 marks

Mark scheme: 18 70 2 M1 for 25 000 × 0.0028 oe

This question in 0580/12 Feb/March 2019

13 On any day, the probability that Marcus will get a seat on the school bus is 0.93 . (a) Write down the probability that he will not get a seat on the school bus today. … [1] (b) There are 200 school days in a year. Work out the expected number of days in a year that Marcus will not get a seat. … [1]

2 marks

Mark scheme: 13(a) 0.07 1 13(b) 14 1 FT their (a)

This question in 0580/13 May/June 2020

17 Kim has a 6-sided spinner numbered 1 to 6. She spins it 63 times and her scores are shown in the table. Score on spinner 1 2 3 4 5 6 Frequency 12 7 15 11 8 10 (a) Find the relative frequency of scoring a 5 with this spinner. … [1] (b) Work out the mean score. … [3]

4 marks

Mark scheme: 17(a) 8 1 or [0].127 or 12.7% 63 17(b) 3.41 or 3.412 to 3.413 3 M1 for 1×12 + 2×7 + 3×15 + 4×11 + 5×8 + 6×10 M1 dep for their 215 ÷ 63 18 7y(2x – y) final answer 2 2 B1 for 7 2 xy  y or y 14 x  7 y    or 7 y  2 x  y  seen then spoilt

This question in 0580/11 May/June 2022

14 Mario tests new cars. The probability that a car is faulty is 0.04 . (a) Find the probability that a car is not faulty. … [1] (b) In one week Mario tests 850 cars. Find the number of cars that are expected to be faulty. … [2]

3 marks

Mark scheme: 14(a) 24 1 0.96 or 96% or final answer 25 14(b) 34 cao 2 M1 for 0.04 × 850 oe

This question in 0580/11 Oct/Nov 2022

22 The probability of passing a driving test is 0.36 . 600 people take this driving test. Work out the expected number of these people that will pass. … [1]

1 marks

Mark scheme: 22 216 1

This question in 0580/12 Feb/March 2023

18 The probability that Tom is late for school is 0.12 . There are 200 school days this year. Work out the expected number of times that Tom is late for school this year. … [1]

1 marks

Mark scheme: 18 24 1

This question in 0580/13 May/June 2023

12 Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Bus Walk Car Other Probability 0.4 0.32 0.17 (a) Complete the table. [2] (b) There are 1800 students at the school. Find the expected number of students that walk to school. … [1]

3 marks

Mark scheme: 12(a) 0.11 oe 2 M1 for 1 – (0.4 + 0.32 + 0.17) oe 12(b) 576 1

This question in 0580/13 Oct/Nov 2023

23 Mai buys two batteries. The probability that a battery is faulty is 1 . 10 First battery Second battery … Faulty Faulty 1 10 Not faulty … … Faulty … Not faulty Not faulty … (a) Complete the tree diagram. [2] (b) Find the probability that Mai buys two faulty batteries. … [2] (c) A shop sells 3000 batteries in one month. Work out the expected number of faulty batteries the shop sells. … [1]

5 marks

Mark scheme: 23(a) 9 1 9 1 9 2 1 1 B1 for and in correct places in 2nd 10 10 10 10 10 10 10 battery 9 or correctly placed for the first battery 10 23(b) 1 2 1 1 oe M1 for their 100 10 10 23(c) 300 1

This question in 0580/12 Feb/March 2025