Introduction to probability — Paper 1 · IGCSE Mathematics 0580

20 Aminata has a bag containing 35 beads. The beads are either blue, yellow or red. One bead is chosen at random. 2 3 The probability of choosing a blue bead is and the probability of choosing a yellow bead is . 7 5 Calculate (a) the number of blue beads in the bag, Answer(a) [2] (b) the probability of choosing a red bead. Answer(b) [2]

4 marks

Mark scheme: 20 (a) 10 2 2 M1 for x 35 7 2 4 2  3  (b) oe or 0.114 (...) + M1 for 1 -   soi or 35  7 5  or 11.4% 3 [35 - (his (a) + x 35] ÷ 35 5 0.11 or 11% seen imply M1

This question in 0580/11 Oct/Nov 2004

2 A bag of 30 sweets contains 8 chocolates, 13 nougats and 9 toffees. A sweet is selected at random. What is the probability that it is a toffee? Answer [1]

1 marks

Mark scheme: 2 9 3 1 isw only for incorrect cancelling or or 0.3 or 30% isw 30 10

This question in 0580/11 May/June 2005

9 (a) A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange. Aminata chooses one piece of fruit at random. What is the probability that she chooses (i) a banana, Answer(a)(i) [1] (ii) a mango? Answer(a)(ii) [1] 5 (b) The probability that it will rain in Switzerland on 1st September is . 12 State the probability that it will not rain in Switzerland on 1st September. Answer(b) [1]

3 marks

Mark scheme: 9 (a) (i) 4 1 oe. 10 (ii) 0 1 (b) 7 1 o.e. 12 5

This question in 0580/11 May/June 2006

23 The diagram shows a six-sided spinner. For Examiner's Use 6 1 5 2 4 3 5 (a) Amy spins a biased spinner and the probability she gets a two is . 36 Find the probability she (i) does not get a two, Answer(a) (i) [1] (ii) gets a seven, Answer(a) (ii) [1] (iii) gets a number on the spinner less than 7. Answer(a) (iii) [1] (b) Joel spins his blue spinner 99 times and gets a two 17 times. Write down the relative frequency of getting a two with Joel’s spinner. Answer(b) [1] 21 (c) The relative frequency of getting a two with Piero’s spinner is . 102 Which of the three spinners, Amy’s, Joel’s or Piero’s, is most likely to give a two? Answer(c) [1]

5 marks

Mark scheme: 23 (a) (i) 3631 oe isw 1 Fraction, decimal or percentage only. (ii) 0 Final ans 1 06 , 360 , 0% or zero. Not allow ‘no’, none, 70 or 0/0. (iii) 1 1 Allow 66 or 3636 or 100%. (b) 1799 isw 1 If decimal, allow art 0.172 (c) Piero’s 1 Can be indicated by 10221 5 Total for the paper is 56 marks

This question in 0580/11 Oct/Nov 2006

20 (a) 85% of the seeds in a packet will produce red flowers. For One seed is chosen at random. Examiner's Use What is the probability that it will not produce a red flower? Answer(a) [1] (b) A box of 15 pencils contains 5 red, 4 yellow and 6 blue pencils. One pencil is chosen at random from the box. Find the probability that it is (i) yellow, Answer(b)(i) [1] (ii) yellow or blue, Answer(b)(ii) [1] (iii) green. Answer(b)(iii) [1]

4 marks

Mark scheme: 20 (a) 15(%) or 0.15 or 10015 oe 1 isw for change of form or cancelling only in all 4 parts. Not ratio. (b) (i) oe cao 1 Allow 0.267 or 0.266(6….) or % form 15 Minimum 3 significant figures 10 (ii) oe cao 1 Allow 0.667 or 0.666(6…) or % form 15 Minimum 3 significant figures Consistent use of wrong denominator in all of (b), −1 once. 0 (iii) 0 or cao 1 Allow nil, none or zero only. No other 15 denominator allowed.

This question in 0580/11 Oct/Nov 2008

3 In a group of 35 students, 14 go to school by bus. Write down the probability that a student, chosen at random, does not go to school by bus. Give your answer as a fraction in its lowest terms. Answer [2]

2 marks

Mark scheme: 3 21 3 2 W1 for 5 35 14 M1 1 − oe 35 2 SC1 answer 5

This question in 0580/11 May/June 2010

17 Simon has ten cards, numbered 1 to 10. He chooses a card at random. Write down the probability that the number on the card is (a) 8, Answer(a) [1] (b) 12, Answer(b) [1] (c) an odd number, Answer(c) [1] (d) not a multiple of 3. Answer(d) [1]

4 marks

Mark scheme: 117 (a) 1 10 0 (b) 0 1 Accept but no other number than 10 10 5 (c) oe 1 10 7 (d) 1 10

This question in 0580/11 Oct/Nov 2010

10 The heights of 43 children are measured to the nearest centimetre. For Braima draws a bar chart from this information. Examiner's Use 16 14 12 10 Frequency 8 6 4 2 0 120-129 130-139 140-149 150-159 160-169 170-179 180-189 Height (centimetres) A child is chosen at random. Write down, as a fraction, the probability that the child will be (a) in the group 140 – 149 cm, Answer(a) [1] (b) less than 160 cm, Answer(b) [1] (c) in the group 160 – 169 cm. Answer(c) [1]

3 marks

Mark scheme: 15 10 (a) cao final answer 1 If zero in (a) and (b) then 43 SC1 if both (a) and (b) are correct decimals or percentages as answers. (Mark as 0 for (a) and SC1 for (b)) 42 (b) cao final answer 1 43 0 (c) 0 or 1 43

This question in 0580/12 Oct/Nov 2010

20 4 4 5 6 8 (a) The diagram shows 5 discs. One disc is chosen at random. (i) Which number is most likely to be chosen? Answer(a)(i) [1] (ii) What is the probability that the number on the disc is even? Answer(a)(ii) [1] (iii) What is the probability that the number on the disc is even and a factor of 20? Answer(a)(iii) [1] (b) A disc is chosen at random from the discs with even numbers. What is the probability that the number on the disc is a factor of 20? Answer(b) [1] Questions 21 and 22 are printed on the next page

4 marks

Mark scheme: 20 (a) (i) 4 1 4 (ii) oe 1 5 2 (iii) oe 1 5 2 (b) oe 1 4

This question in 0580/13 Oct/Nov 2010

3 A letter is chosen at random from the following word. S T A T I S T I C S Write down the probability that the letter is (a) A or I , Answer(a) [1] (b) E. Answer(b) [1]

2 marks

Mark scheme: 3 3 1 (a) or 0.3 or 30% 10 1 0 (b) 0 or or 0% 10

This question in 0580/12 May/June 2011

20 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. For Examiner's Each car only uses one type of fuel. Use Petrol Diesel Liquid Hydrogen Electricity 40 12 2 6 (a) Write down the mode. Answer(a) [1] (b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2] (c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]

5 marks

Mark scheme: 20 (a) Petrol cao 1 (b) 72 2 M1 for 360 × 12 ÷ 60 1 6 3 2 (c) 2 B1 or or or 0.1 or 10% 10 60 30 20

This question in 0580/12 Oct/Nov 2011

5 For 1 During April the probability that it will rain on any one day is . Examiner's 6 Use On how many of the 30 days in April would it be expected to rain? Answer [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 25 1

This question in 0580/13 Oct/Nov 2011

20 (a) Colin has some seeds. For The probability a seed will grow is 0.85 . Examiner's Use Find the probability that a seed will not grow. Answer(a) [1] (b) Richard grows flowers. Some of his flowers are chosen at random. The colours are recorded in the table below. Colour of Relative Frequency flower Frequency Red 20 0.16 Blue 15 Yellow 35 Other 55 (i) Complete the table to show the relative frequency of each colour. [2] (ii) Richard grows 800 flowers in total. Estimate how many of these flowers are red. Answer(b)(ii) [2]

5 marks

Mark scheme: 20 (a) [0].15 oe 1 (b) (i) 0.12, 0.28, 0.44 oe 2 M1 for division of 15, 35 or 55 by their 125 Or B1 for 1 correct (ii) 128 2 M1 for 800 × [0].16

This question in 0580/13 May/June 2012

5 A bowl of fruit contains only 8 peaches, 5 oranges and 6 apples. For One piece of fruit is chosen at random. Examiner's Use Write down the probability that it is (a) an orange, Answer(a) [1] (b) not a peach. Answer(b) [1]

2 marks

Mark scheme: 5 5 (a) oe 1 0.263 19 11 1 0.579 or 0.5789 (b) oe 19

This question in 0580/12 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

20 Marco throws a six-sided dice 27 times. For Examiner's The bar chart shows his results. Use 8 7 6 5 Frequency 4 3 2 1 0 1 2 3 4 5 6 Score on dice (a) Write down the mode. Answer(a) … [1] (b) Work out the probability that Marco throws a number less than 5. Answer(b) … [2] (c) Calculate the mean. Answer(c) … [3]

6 marks

Mark scheme: 20 (a) 4 cao 1 (b) 21 2 M1 for 3 + 6 + 5 + 7 + 4 or 21 seen 27 oe isw (c) 3.33(3…) 3 M1 for 3 × 1 + 6 × 2 + 5 × 3 + 7 × 4 + 4 × 5 + 2 × 6, allow one incorrect product or 90 seen and M1 dep for ‘their 90’ ÷ 27

This question in 0580/11 May/June 2013

9 The probability that the school hockey team will win its next match is 0.45 . The probability that it will lose its next match is 0.3 . Work out the probability that the school hockey team will draw its next match. Answer … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 9 0.25 oe 2 M1 for 1– (0.45 + 0.3) or better or SC1 for 0.52 as final answer 24 

This question in 0580/12 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

18 (a) The probability that FC Victoria wins the cup is 0.18 . Work out the probability that they do not win the cup. Answer(a) … [1] (b) After training, the shirts are washed. There are 5 red, 3 blue and 6 green shirts. One shirt is taken from the washing machine at random. Find the probability that it is (i) red, Answer(b)(i) … [1] (ii) blue or green, Answer(b)(ii) … [1] (iii) white. Answer(b)(iii) … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 18 (a) (0).82 oe 1 5 (b) (i) oe 1 in (b) penalise consistent incorrect 14 denominator once 9 (ii) oe 1 14 (iii) 0 1 IGCSE – May/June 2014 0580 12

This question in 0580/12 May/June 2014

15 Celine buys a bag of 24 tulip bulbs. There are 8 red bulbs and 5 white bulbs. All of the other bulbs are yellow. Celine chooses a bulb at random from the bag. (a) Write down the probability that the bulb is red or white. Answer(a) … [1] (b) Write down the probability that the bulb is yellow. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 13 15 (a) oe 1 24 11 (b) oe 1 24 7 7 3 4

This question in 0580/13 May/June 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

15 Chico has a bag of sweets. He takes a sweet from the bag at random. The table shows the probabilities of taking each flavour of sweet. Flavour Lemon Lime Strawberry Blackcurrant Orange Probability 0.15 0.22 0.18 0.24 (a) Complete the table. [2] (b) Find the probability that the sweet is lemon or lime. Answer(b) … [1] __________________________________________________________________________________________

3 marks

Mark scheme: 15 (a) [0].21 oe 2 M1 for 1 – ([0].15 + [0].22 + [0].18 + [0].24) or 100 – (15 + 22 + 18 + 24) (b) [0].37 oe 1

This question in 0580/11 Oct/Nov 2015

16 The probability that it will rain on any day is . 5 Calculate an estimate of the number of days it will rain in a month with 30 days. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 6 6 1

This question in 0580/13 Oct/Nov 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

3 In a group of students the probability that a student is left-handed is 0.28 . A student is chosen at random from the group. Find the probability that this student is not left-handed. … [1]

1 marks

Mark scheme: 3 [0].72 oe 1

This question in 0580/11 May/June 2016

13 (a) A bag contains 16 counters. 4 of the counters are blue. A counter is taken from the bag at random. On the probability scale, draw an arrow (↓) to show the probability that this counter is blue. 0 0.5 1 [1] (b) Another bag contains 5 black counters, 8 white counters, 6 green counters and 1 yellow counter. A counter is taken from this bag at random. Find the probability that this counter is (i) white, … [1] (ii) not white. … [1]

3 marks

Mark scheme: 13 (a) Arrow 2 cm from 0 1 8 (b) (i) 1 oe 20 12 (ii) 1FT FT 1 – their (b)(i) provided their (b)(i) < 1 oe 20

This question in 0580/12 May/June 2016

17 The table shows the number of screws of different lengths in a box of 100 screws. Length (mm) 20 40 50 60 Number of screws 18 36 24 22 A screw is chosen at random from the box. Find the probability that the screw has length (a) 50 mm, … [1] (b) less than 60 mm, … [2] (c) 70 mm. … [1]

4 marks

Mark scheme: 24 17 (a) oe 1 100 78 18 + 36 + 24 22 (b) oe 2 M1 for or 1 − 100 100 100 (c) 0 1

This question in 0580/13 May/June 2016

11 E L E P H A N T Francesca chooses a letter at random from this word. (a) Write down the letter she is most likely to choose. … [1] (b) Write down the probability that she chooses the letter R. … [1]

2 marks

Mark scheme: 11 (a) E 1 (b) 0 or zero 1

This question in 0580/11 Oct/Nov 2016

4 A bag contains 20 counters. 10 counters are red, 8 are blue and the rest are yellow. One counter is taken from the bag at random. (a) Mark an arrow on the probability scale to show the probability that the counter is red. 0 1 [1] (b) Find the probability that the counter is yellow. … [1]

2 marks

Mark scheme: 4 (a) Correct arrow 1 2 (b) oe or 0.1 or 10% 1 20

This question in 0580/12 Oct/Nov 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

16 (a) A bag contains 3 red, 5 blue and 4 green counters. A counter is picked at random. Work out the probability that the counter is (i) blue, … [1] (ii) yellow. … [1] (b) The probability of picking a brown counter from another bag is 0.35 . Work out the probability of not picking a brown counter. … [1]

3 marks

Mark scheme: 5 16 (a) (i) oe 1 12 (ii) 0 1 (b) [0].65 oe 1

This question in 0580/13 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

2 The probability that Stephanie wins her next tennis match is 0.85 . Find the probability that Stephanie does not win her next tennis match. … [1]

1 marks

Mark scheme: 2 [0].15 oe 1

This question in 0580/12 May/June 2017

13 Bastian has a bag containing four types of sweet. He takes a sweet from the bag at random. Sweet Mint Fruit Toffee Chocolate Probability 0.15 0.3 0.2 Complete the table. [2]

2 marks

Mark scheme: 13 [0].35 2 M1 for 1 – (0.15 + 0.3 + 0.2)

This question in 0580/12 Oct/Nov 2017

6 A bag contains 16 counters. 3 are red, 6 are blue and the rest are yellow. Jay takes a counter from the bag at random. (a) Write down the colour Jay is most likely to take. … [1] (b) Write down the probability that the counter is red. … [1]

2 marks

Mark scheme: 6(a) Yellow 1 6(b) 3 1 or 0.1875 or 18.75% 16

This question in 0580/13 Oct/Nov 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

12 The probability that Kim wins a game is 0.72 . In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win. … [2]

2 marks

Mark scheme: 12 162 2 M1 for 225 × 0.72 oe

This question in 0580/13 May/June 2018

8 A bag contains 50 counters. 10 of the counters are red. One of the counters is taken from the bag at random. (a) Draw an arrow ( ) on the scale to show the probability that this counter is red. 0 0.5 1 [1] (b) Find the probability that the counter is not red. … [1]

2 marks

Mark scheme: 8(a) Arrow at 0.2 1 8(b) 0.8 oe 1

This question in 0580/11 Oct/Nov 2018

11 (a) A bag contains 6 blue counters and 2 red counters only. A counter is taken from the bag at random. Draw an arrow (↓) on the probability scale to show the probability of taking (i) a blue counter, 0 1 [1] (ii) a yellow counter. 0 1 [1] (b) Another bag contains green counters and black counters only. A counter is taken from the bag at random. The probability of taking a green counter is 0.64 . Work out the probability of taking a black counter. … [1]

3 marks

Mark scheme: 11(a)(i) 3 1 Clear indication Arrow at 4 11(a)(ii) Arrow at 0 1 Clear indication 11(b) [0].36 oe 1

This question in 0580/12 Oct/Nov 2018

15 Ethan has a box of toys. He takes a toy at random. Toy Car Train Bus Other Probability 0.2 0.45 0.08 Complete the table. [2]

2 marks

Mark scheme: 15 0.27 oe 2 M1 for 1 − (0.2 + 0.45 + 0.08) oe

This question in 0580/13 Oct/Nov 2018

2 The probability that it will be sunny tomorrow is 0.97 . Work out the probability that it will not be sunny tomorrow. … [1]

1 marks

Mark scheme: 2 [0].03 oe 1

This question in 0580/12 Feb/March 2019

4 A bag contains green balls and red balls only. A ball is taken at random from the bag. The probability of taking a green ball is 0.38 . Write down the probability of taking (a) a red ball, … [1] (b) a blue ball. … [1]

2 marks

Mark scheme: 4(a) [0].62 oe 1 4(b) 0 1

This question in 0580/11 May/June 2019

15 A box contains 22 coloured pencils. 6 pencils are pink, 9 pencils are blue and 7 pencils are yellow. (a) Write down the ratio pink pencils : not pink pencils. Give your answer in its simplest form. … : … [2] (b) A pencil is taken at random from the box. Write down the probability that this pencil is green. … [1]

3 marks

Mark scheme: 15(a) 3 : 8 cao 2 B1 for 6 : 16 or 8 2 3 1: or 1:2 or 1:2.67 or :1 or 0.375:1 3 3 8 If 0 scored, SC1 for 8 : 3 15(b) 0 1

This question in 0580/12 May/June 2019

6 The probability that Alex wins a prize is 0.27 . Find the probability that Alex does not win a prize. … [1]

1 marks

Mark scheme: 6 0.73 oe 1

This question in 0580/13 May/June 2019

5 Rui has a bag containing 5 black pens, 8 red pens and 3 blue pens only. He takes a pen out of the bag at random. Draw an arrow ( . ) on the probability scale to show the probability that Rui takes (a) a red pen, 0 1 [1] (b) a red pen or a blue pen. 0 1 [1]

2 marks

Mark scheme: 5(a) 1 1 Arrow at 2 5(b) 11 1 Arrow at 16

This question in 0580/11 Oct/Nov 2019

5 A bag contains 3 green balls, 4 red balls and 1 blue ball only. Matt takes a ball from the bag at random. Some probabilities are marked on the probability scale. A B C D E F G H I 0 0.5 1 Write down the letter that shows the probability that (a) Matt takes a red ball, … [1] (b) Matt does not take a blue ball. … [1]

2 marks

Mark scheme: 5(a) E cao 1 5(b) H cao 1

This question in 0580/12 Oct/Nov 2019

8 A bag contains 6 red balls and 10 blue balls only. On the probability scale, draw an arrow ( ) to show the probability that a ball taken at random is (a) blue, 0 1 1 2 [1] (b) red or blue. 0 1 1 2 [1]

2 marks

Mark scheme: 8(a) 5 1 indication at cao 8 8(b) indication at 1 cao 1

This question in 0580/13 Oct/Nov 2019

5 The diagram shows a fair 8-sided spinner. The numbers on the spinner are 3, 4, 4, 7, 7, 7, 8 and 9. (a) The spinner is spun once. Write down the probability that the spinner lands on (i) the number 7, … [1] (ii) a number greater than 2. … [1] (b) The spinner is spun 160 times. Work out the expected number of times the spinner lands on the number 7. … [1]

3 marks

Mark scheme: 5(a)(i) 3 1 oe 8 5(a)(ii) 1 1 5(b) 60 1 FT their (a)(i)

This question in 0580/12 Feb/March 2020

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

4 A bag contains 20 balls. 5 of these balls are red. A ball is picked at random from the bag. On the probability scale, draw an arrow ( ) to show the probability that this ball is red. 0 0.5 1 [1]

1 marks

Mark scheme: 4 Arrow at 0.25 1

This question in 0580/12 Oct/Nov 2020

16 A bag contains 7 red discs, 5 green discs and 2 pink discs. Helen takes one disc at random, records the colour and replaces it in the bag. She does this 140 times. Find how many times she expects to take a green disc. … [2]

2 marks

Mark scheme: 16 50 2 5 140 M1 for [× 140] or [×5] 7 + 5 + 2 7 + 5 + 2

This question in 0580/13 Oct/Nov 2020

7 The probability that a train is late is 0.15 . Write down the probability that the train is not late. … [1]

1 marks

Mark scheme: 7 0.85 oe 1

This question in 0580/11 May/June 2021

710 The probability that Jane wins a game is . 10 Find the probability that Jane does not win the game. … [1]

1 marks

Mark scheme: 10 3 1 oe 10

This question in 0580/12 May/June 2021

12 Francesca spins a four-sided spinner numbered 1, 2, 3 and 4. The table shows some of the probabilities of landing on each number. Number 1 2 3 4 Probability 0.18 0.21 0.37 Complete the table. [2]

2 marks

Mark scheme: 12 [0].24 2 M1 for 1 – ([0].18 + [0].21 + [0].37)

This question in 0580/13 May/June 2021

24 Yasmin has 4 white flowers, 3 red flowers and x yellow flowers. She picks a flower at random. The probability that it is white is 1. 5 Find the probability that it is yellow. … [4]

4 marks

Mark scheme: 24 13 4 B3 for [x =] 13 oe 20 or M2 for x + 3 + 4 = 4 × 5 oe or 4 × 5 – 4 – 3 1 4 or M1 for 4 × 5 or = 5 4 + 3 + x

This question in 0580/12 Oct/Nov 2021

5 Cheng spins a fair 6-sided spinner numbered 1 to 6. On the probability scale, draw an arrow ( ) to show the probability that the spinner lands on 4. 0 1 [1]

1 marks

Mark scheme: 5 Arrow at first mark 1

This question in 0580/13 Oct/Nov 2021

9 The probability that it rains tomorrow is 0.47 . Find the probability that it does not rain tomorrow. … [1]

1 marks

Mark scheme: 9 0.53 oe 1

This question in 0580/13 Oct/Nov 2021

13 A 4-sided spinner is numbered 1, 2, 3 and 4. The table shows the probability of the spinner landing on 1, 2 and 4. Number 1 2 3 4 Probability 0.27 0.18 0.32 Complete the table. [2]

2 marks

Mark scheme: 13 [0].23 oe 2 M1 for 1 − [0].27 − [0].18 − [0].32 oe

This question in 0580/11 May/June 2022

5 The probability of picking a red sweet from a bag is 0.05 . Find the probability of not picking a red sweet. … [1]

1 marks

Mark scheme: 5 0.95 oe 1

This question in 0580/13 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

11 A 4-faced dice is numbered 1 to 4. The table shows some of the probabilities of scoring each number. Number 1 2 3 4 Probability 0.17 0.28 0.31 Complete the table. [2]

2 marks

Mark scheme: 11 [0].24 2 M1 for 1 – 0.17 – 0.28 – 0.31oe

This question in 0580/12 Oct/Nov 2022

17 (a)  = { people in a group} B = { people who own a bicycle} C = { people who own a car} There are 120 people in the group. 21 people own a bicycle. 15 people own both a bicycle and a car. 35 people do not own a bicycle and do not own a car. B C (i) Complete the Venn diagram. [2] (ii) A person from the group is chosen at random. Find the probability that this person owns a car. … [1] (b) D E Shade the region D , E . [1]

4 marks

Mark scheme: 17(a)(i) 2 B1 for two numbers in the correct places 17(a)(ii) 79 1 FT their diagram for 79 oe 120 17(b) 1

This question in 0580/12 Oct/Nov 2022

15 Eric has four colours of paint. The table shows the probability that he uses each colour. Colour Red Blue Green Yellow Probability 0.3 0.35 0.13 x Find the value of x. x = … [2]

2 marks

Mark scheme: 15 0.22 oe 2 M1 for 1 – (0.3 + 0.35 + 0.13) oe or B1 for 0.78 oe

This question in 0580/11 May/June 2023

12 A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Letter on A B C D spinner Probability 0.2 0.05 0.35 Complete the table. [2]

2 marks

Mark scheme: 12 0.4 oe 2 M1 for 1 – (0.2 + 0.05 + 0.35) oe or B1 for 0.6 oe

This question in 0580/12 May/June 2023

21 A spinner has five sides. Each side is painted red, blue, green, yellow or orange. The table shows some of the probabilities of the spinner landing on each colour. Colour Red Blue Green Yellow Orange Probability 0.3 0.16 0.18 0.25 (a) Complete the table. [2] (b) Dan spins the spinner once. Find the probability that the spinner lands on red or blue. … [2]

4 marks

Mark scheme: 21(a) 0.11 oe 2 M1 for 1 – (0.3 + 0.16 + 0.18 + 0.25) oe or B1 for 0.89 oe 21(b) 0.46 oe 2 M1 for 0.3 + 0.16

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

19 (a) A bag contains these cards. 1 7 3 9 4 5 2 One of these cards is picked at random. Find the probability that the number on the card is greater than 3. … [1] (b) A box contains 3 blue cards and 7 red cards. Kim picks one card at random, notes its colour and then replaces it in the box. She then picks another card at random. (i) Complete the tree diagram. First card Second card 3 Blue 10 Blue 3 10 Red … 3 Blue 10 … Red Red … [1] (ii) Work out the probability that both of the cards Kim picks are blue. … [2]

4 marks

Mark scheme: 19(a) 4 1 oe 7 19(b)(i) 7 1 in each space on tree diagram 10 19(b)(ii) 9 2 3 3 oe M1 for  oe 100 10 10

This question in 0580/13 Oct/Nov 2023

13 There are 20 cars in a car park and 3 of the cars are blue. (a) James wants to draw a pie chart to show this information. Find the angle of the sector for the blue cars in this pie chart. … [2] (b) One of the 20 cars is picked at random. Find the probability that this car is not blue.

3 marks

Mark scheme: 13(a) 54 2 3 M1 for [ 360 ] oe or 360[ 3 ] oe 20 20 13(b) 17 1 oe 20

This question in 0580/12 Feb/March 2024

11 Geetha has a box of toys. She picks a toy at random from the box. The probability that she picks a wooden toy is 0.6 . (a) Work out the probability that she does not pick a wooden toy. … [1] (b) The box contains three types of toys, wooden, plastic or metal. Type of toy Wooden Plastic Metal Number of toys 14 14 Probability 0.6 Complete the table. [2]

3 marks

Mark scheme: 11(a) 0.4 oe 1 11(b) 42 2 B1 for 42 0.2 0.2 B1 for 0.2 and 0.2 If B0 scored, SC1 for their two probabilities each being half of their (a)

This question in 0580/11 May/June 2024

8 In a city, the probability that it will rain today is 0.15 . Find the probability that it will not rain today in this city. … [1]

1 marks

Mark scheme: 8 0.85 oe 1

This question in 0580/13 May/June 2024

5 A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball from the bag at random. A B C D E F G 0 1 Write down the letter from the probability scale that shows the probability that (a) Zia takes a green ball … [1] (b) Zia takes a yellow ball … [1] (c) Zia does not take a blue ball. … [1]

3 marks

Mark scheme: 5(a) C 1 5(b) A 1 5(c) F 1

This question in 0580/13 Oct/Nov 2024

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

24 % = {students in a year group} H = {students who study History} G = {students who study Geography} 80 students are in the year group. 40 students study History. % H G 10 15 (a) Complete the Venn diagram. [2] (b) Find n(G). … [1] (c) A student is chosen at random. Work out the probability that the student does not study History and does not study Geography. … [1]

4 marks

Mark scheme: 24(a) 2 B1 for one correct value correctly placed If 0 scored, SC1 for two positive integers such that n(G) = 55 24(b) 55 1 FT their 30 + their 25 provided their 30 + their 25 is less than 80 24(c) 15 1 oe 80

This question in 0580/11 Oct/Nov 2025

7 A bag contains 8 discs numbered 1 to 8. A disc is picked at random from the bag. 0 1 On the probability scale, draw an arrow ( ) to show the probability that the number is (a) an even number, label the arrow A [1] (b) 9, label the arrow B [1] (c) less than 3, label the arrow C. [1]

3 marks

Mark scheme: 7(a) Arrow labelled A on 0.5 1 7(b) Arrow labelled B on 0 1 7(c) Arrow labelled C on 0.25 1

This question in 0580/12 Oct/Nov 2025

10 A bag contains red balls and green balls. They are in the ratio red balls : green balls = 2 : 3. A ball is picked at random. Find the probability that it is a red ball. … [1]

1 marks

Mark scheme: 10 2 1 oe 5

This question in 0580/12 Oct/Nov 2025

26 There are 2 sets of traffic lights on Li’s journey to work. The probability he stops at the first set of traffic lights is 0.4 . The probability he stops at the second set of traffic lights is 0.7 . First set of traffic lights Second set of traffic lights Stops … Stops 0.4 … Does not stop Stops … … Does not stop … Does not stop (a) Complete the tree diagram. [2] (b) Work out the probability that Li does not stop at both sets of traffic lights. … [2] Question 27 is printed on the next page.

4 marks

Mark scheme: 26(a) Correct tree diagram 2 B1 for 0.6 on the first branch or 0.7 and 0.3 correct on all second branches 26(b) 0.18 oe 2 FT their tree diagram for 2 marks M1 for their 0.6 × their 0.3

This question in 0580/13 Oct/Nov 2025