Introduction to probability — Paper 2 · IGCSE Mathematics 0580

20 A gardener plants seeds from a packet of 25 seeds. For 14 of the seeds will give red flowers and 11 will give yellow flowers. Examiner's The gardener chooses two seeds at random. Use (a) Write the missing probabilities on the tree diagram below. First seed Second seed 13 24 Red 14 Red 25 … Yellow … Red 11 Yellow 25 … Yellow [2] (b) What is the probability that the gardener chooses two seeds which will give (i) two red flowers, Answer(b)(i) [2] (ii) two flowers of a different colour? Answer(b)(ii) [2]

6 marks

Mark scheme: 20 11 14 10 2 B1 any 2 correct and ISW (a) 24 24 24 91 (b) (i) o.e (= 0.303) 2* M1 14 x 13 only 300 25 24 77 (ii) o.e (= 0.513) 2* M1 for adding their R x Y and 150 Y x R probabilities

This question in 0580/21 Oct/Nov 2004

2 In a group of 30 students, 18 have visited Australia, 15 have visited Botswana and 5 have not visited either country. Work out the number of students who have visited Australia but not Botswana. Answer [2]

2 marks

Mark scheme: 2 10 2 M1 33 – 25 M1 30 – 15 – 5 oe or 38 – 30 with no further working J

This question in 0580/22 Oct/Nov 2010

17 Boys Girls Total Asia 62 28 Europe 35 45 Africa 17 Total 255 For a small international school, the holiday destinations of the 255 students are shown in the table. (a) Complete the table. [3] (b) What is the probability that a student chosen at random is a girl going on holiday to Europe? Answer(b) [1]

4 marks

Mark scheme: 17 (a) 3 B1 two or three correct Boys Girls Total or B2 four or five correct Asia 62 28 90 Europe 35 45 80 Africa 68 17 85 Total 165 90 255 3 45 15 9 (b) or 0.176(47…) 1 Allow , , 17 255 85 51 14 0 ( ) − 

This question in 0580/22 Oct/Nov 2010

15 A teacher asks 36 students which musical instruments they play. ForFor Examiner'sExaminer's P = {students who play the piano} UseUse G = {students who play the guitar} D = {students who play the drums} The Venn diagram shows the results. P G x 2 8 1 5 4 7 5 D (a) Find the value of x. Answer(a) x = [1] (b) A student is chosen at random. Find the probability that this student (i) plays the drums but not the guitar, Answer(b)(i) [1] (ii) plays only 2 different instruments. Answer(b)(ii) [1] (c) A student is chosen at random from those who play the guitar. Find the probability that this student plays no other instrument. Answer(c) [1]

4 marks

Mark scheme: ( ) 15 (a) 4 1 12 (b) (i) oe 0.333 1 36 11 (ii) , 0.306 or 0.3055 to 1 36 0.3056 1 8 (c) oe 0.533(3…) 15 k 2

This question in 0580/21 May/June 2011

16 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: 16 (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 0580/22 Oct/Nov 2011

12 For Examiner′s 2 Use 1 3 5 R F 11 students are asked if they like rugby (R) and if they like football (F). The Venn diagram shows the results. (a) A student is chosen at random. What is the probability that the student likes rugby and football? Answer(a) … [1] (b) On the Venn diagram shade the region R' ∩ F' . [1] _____________________________________________________________________________________

2 marks

Mark scheme: 12 (a) 3 1 11 (b) 1

This question in 0580/21 May/June 2013

2 The Ocean View Hotel has 300 rooms numbered from 100 to 399. A room is chosen at random. Find the probability that the room number ends in zero. Answer … [2] _____________________________________________________________________________________

2 marks

Mark scheme: 30 k 2 oe www 2 M1 for 30 seen or seen 300 300

This question in 0580/23 May/June 2013

12 Two spinners have sections numbered from 1 to 5. Each is spun once and each number is equally likely. The possibility diagram is shown below. 5 4 1 Second 2 3 5 spinner 1 2 3 4 2 3 5 4 1 1 2 3 4 5 First spinner Find the probability that (a) both spinners show the same number, Answer(a) … [2] (b) the sum of the numbers shown on the two spinners is 7. Answer(b) … [2] _____________________________________________________________________________________

4 marks

Mark scheme: 12 (a) 5 5 k oe 2 B1 for answer or 25 k 25 4 4 k (b) oe 2 B1 for answer or 25 k 25 8x

This question in 0580/23 May/June 2013

6 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 6 (a) oe 1 6 (b) 200 1FT FT 600 × their (a) providing their (a) is a probability

This question in 0580/21 Oct/Nov 2013

22 For Examiner′s Use R T 15 5 11 19 The Venn diagram shows the number of red cars and the number of two-door cars in a car park. There is a total of 50 cars in the car park. R = {red cars} and T = {two-door cars}. (a) A car is chosen at random. Write down the probability that (i) it is red and it is a two-door car, Answer(a)(i) … [1] (ii) it is not red and it is a two-door car. Answer(a)(ii) … [1] (b) A two-door car is chosen at random. Write down the probability that it is not red. Answer(b) … [1] (c) Two cars are chosen at random. Find the probability that they are both red. Answer(c) … [2] (d) On the Venn diagram, shade the region R ∪ T '. [1] _____________________________________________________________________________________

6 marks

Mark scheme: 5 22 (a) (i) oe 1 50 11 (ii) oe 1 50 11 (b) oe 1 16 380 20 19 (c) oe 2 M1 for × 2450 50 49 (d) 1

This question in 0580/21 Oct/Nov 2013

20 During one day 48 people visited a museum. For Examiner′s The length of time each person spent in the museum was recorded. Use The results are shown on the cumulative frequency diagram. 50 40 30 Cumulative frequency 20 10 0 1 2 3 4 5 6 Time (hours) Work out (a) the median, Answer(a) … h [1] (b) the 20th percentile, Answer(b) … h [2] (c) the inter-quartile range, Answer(c) … h [2] (d) the probability that a person chosen at random spends 2 hours or less in the museum. Answer(d) … [2] _____________________________________________________________________________________ Question 21 is printed on the next page.

7 marks

Mark scheme: 20 (a) 4.05 to 4.2 1 (b) 2.6 to 2.75 2 B1 for 9.6 seen (c) 2.05 to 2.25 2 B1 for [UQ] 5.0 to 5.1 and [LQ] 2.85 to 2.95 seen 5 (d) 2 M1 for 5 48 4× sin 65

This question in 0580/22 Oct/Nov 2013

18 A gardener measured the lengths of 50 green beans from his garden. For Examiner′s The results have been used to draw this cumulative frequency diagram. Use 50 40 30 Cumulative frequency 20 10 0 5 10 15 20 25 30 35 Length of green bean (cm) Work out (a) the median, Answer(a) … cm [1] (b) the number of green beans that are longer than 26 cm, Answer(b) … [2] (c) the inter-quartile range, Answer(c) … cm [2] (d) the probability that a green bean chosen at random is more than 14 cm long. Answer(d) … [2] _____________________________________________________________________________________ Question 19 is printed on the next page.

7 marks

Mark scheme: 18 (a) 19–19.1 1 (b) 3 2 M1 for 47 seen (c) 4.9 to 5.7 2 B1 for [UQ] 21.7 to 22.2 and [LQ] 16.5 to 16.8 45 2 B1 for 45 seen or (d) oe 50 5 SC1 for isw 50

This question in 0580/23 Oct/Nov 2013

22 P Q f i k g j h n m (a) Use the information in the Venn diagram to complete the following. (i) P ∩ Q = { … } [1] (ii) P' ∪ Q = { … } [1] (iii) n(P ∪ Q)' = … [1] (b) A letter is chosen at random from the set Q. Find the probability that it is also in the set P. Answer(b) … [1] (c) On the Venn diagram shade the region P' ∩ Q. [1] (d) Use a set notation symbol to complete the statement. {f, g, h} … P [1]

6 marks

Mark scheme: 22 ((a) i, jj 1 i, jj, k,, mm, n 1 ( 2 1 ((b) 2 1 3 ((c) 1 PP Q ((d) ⊂ orr ⊆⊆ 1

This question in 0580/22 May/June 2014

18 If it rains today the probability that it will rain tomorrow is 0.4 . If it does not rain today the probability that it will rain tomorrow is 0.2 . On Sunday it rained. (a) Complete the tree diagram for Monday and Tuesday. Monday Tuesday Rain 0.4 Rain 0.4 0.6 No rain Rain … … No rain … No rain [2] (b) Find the probability that it rains on at least one of the two days shown in the tree diagram. Answer(b) … [3] __________________________________________________________________________________________

5 marks

Mark scheme: 18 (a) 6.0 2.0 8.0 in correct places 2 B1 for 0.6 in correct place B1 for 0.2 and 0.8 in correct places (b) 0.52 oe nfww 3 M2FT for 1 – (their 0.6 × their 0.8) oe or M1FT for a correct product from their tree in (a)

This question in 0580/21 Oct/Nov 2014

16 (a) In this part, you may use this Venn diagram to help you answer the questions. F S In a class of 30 students, 25 study French (F), 18 study Spanish (S). One student does not study French or Spanish. (i) Find the number of students who study French and Spanish. Answer(a)(i) … [2] (ii) One of the 30 students is chosen at random. Find the probability that this student studies French but not Spanish. Answer(a)(ii) … [1] (iii) A student who does not study Spanish is chosen at random. Find the probability that this student studies French. Answer(a)(iii) … [1] (b) P Q R On this Venn diagram, shade the region R (P Q )′. [1]

5 marks

Mark scheme: 16 (a) (i) 14 2 M1 for any two of 1, 11, 14, 4 correctly placed on Venn diagram or for 1 + 25 − x + x + 18 − x = 30 oe 11 25 − their (a )(i ) their 11 (ii) oe 1FT FT or from 30 30 30 diagram 11 their 11 (iii) oe 1FT FT their diagram e.g. 12 12 25 − their (a )(i ) or 12 (b) 1

This question in 0580/23 May/June 2015

20 The table shows the probability that a person has blue, brown or green eyes. Eye colour Blue Brown Green Probability 0.4 0.5 0.1 Use the table to work out the probability that two people, chosen at random, (a) have blue eyes, Answer(a) … [2] (b) have different coloured eyes. Answer(b) … [4] __________________________________________________________________________________________

6 marks

Mark scheme: 20 (a) 0.16 oe 2 M1 for 4.0 × 4.0 If zero scored SC1 for fully correct evaluated method involving a without replacement method (b) 0.58 oe 4 M3 for 1 − ( 4.0 2 + 5.0 2 + 1.02 ) oe or M2 for 4.0 2 + 5.0 2 + 1.0 2 ALT method M3 for 4.0 × ( 5.0 + )1.0 + 5.0 × ( 4.0 + )1.0 + 1.0 × ( 4.0 + 5.0) oe or M2 for addition of any three of: 4.0 × ,5.0 4.0 × ,1.0 5.0 × ,4.0 0.5 × 0.1, 1.0 × 4.0 and 1.0 × 5.0 or M1 for addition of any two of: 4.0 × ,5.0 4.0 × ,1.0 5.0 × ,4.0 5.0 × ,1.0 1.0 × 4.0 and 1.0 × 5.0 If zero scored SC2 for fully correct evaluated method involving a without replacement method [ ]

This question in 0580/21 Oct/Nov 2015

23 A box contains 6 red pencils and 8 blue pencils. A pencil is chosen at random and not replaced. A second pencil is then chosen at random. (a) Complete the tree diagram. First pencil Second pencil Red … Red 6 14 8 13 Blue Red … … Blue … Blue [2] (b) Calculate the probability that (i) both pencils are red, Answer(b)(i) … [2] (ii) at least one of the pencils is red. Answer(b)(ii) … [3]

7 marks

Mark scheme: 8 523 (a) and 1 14 13 6 7 1 and 13 13 30 (b) (i) oe 2 M1FT for 6 × 5 182 14 their13 126 (ii) oe 3 M2FT for 182 8 7 1 − × 14 13 6 5 6 8 8 6 or × + + × 14 13 14 ×13 14 13 6 8 6 or + × oe 14 14 13 or M1FT for sum of any two of 6 5 6 8 8 6 × or × or 14 13 14 13 14 ×13

This question in 0580/22 Oct/Nov 2015

4 The probability that it will rain on any day is 15 . Calculate an estimate of the number of days it will rain in a month with 30 days. Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 4 6 1

This question in 0580/23 Oct/Nov 2015

21 Dan either walks or cycles to school. The probability that he cycles to school is 1 . 3 (a) Write down the probability that Dan walks to school. … [1] (b) When Dan cycles to school the probability that he is late is 1 . 8 When Dan walks to school the probability that he is late is 3 . 8 Complete the tree diagram. 1 Late 8 Cycles 1 3 Not late … Late 3 8 … Walks Not late … [2] (c) Calculate the probability that (i) Dan cycles to school and is late, … [2] (ii) Dan is not late. … [3]

8 marks

Mark scheme: 2 21 (a) oe 1 3 2 7 5 7 5 (b) their , , oe 2 B1 for either or 3 8 8 8 8 1 1 1 (c) (i) oe 2 M1 for × seen 24 3 8 17 1 7 2 5 (ii) oe 3 M2FT for × + × 24 3 8 3 8 1 7 2 5 or M1FT for × or × 3 8 3 8

This question in 0580/22 Feb/March 2016

22 A B 3 7 12 5 The Venn diagram shows the numbers of elements in each region. (a) Find n(A Bl ) . … [1] (b) An element is chosen at random. Find the probability that this element is in set B. … [1] (c) An element is chosen at random from set A. Find the probability that this element is also a member of set B. … [1] (d) On the Venn diagram, shade the region (A B) l. [1]

4 marks

Mark scheme: 22 (a) 3 1 19 (b) oe 1 27 7 (c) oe 1 10 (d) 1

This question in 0580/21 May/June 2016

11 Hattie has a box of coloured pens. She takes a pen at random from the box. The probability that she takes a red pen is 0.4 . (a) Work out the probability that she does not take a red pen. … [1] (b) The box contains only blue, red and green pens. There are 15 blue pens and 15 green pens. Complete the table. Colour of pen Blue Red Green Number of pens 15 15 Probability 0.4 [2]

3 marks

Mark scheme: 11 (a) 0.6 oe 1 (b) 20 2 B1 for 20 0.3 oe 0.3 oe B1 for 0.3 oe and 0.3 oe

This question in 0580/23 May/June 2016

22 (a) n() = 10, n(A) = 7, n(B) = 6, n ( A , B) l = 1. A B (i) Complete the Venn diagram by writing the number of elements in each subset. [2] (ii) An element of  is chosen at random. Find the probability that this element is an element of Al + B . … [1] (b) On the Venn diagram below, shade the region C l + D l. C D [1]

4 marks

Mark scheme: 22 (a) (i) 2 B1 for n( A ∩ B ) = 4 A B 3 4 2 1 2 their 2 (ii) oe 1FT allow correct answer or FT 10 10 (b) C D 1  3  2

This question in 0580/21 Oct/Nov 2016

15 F M 8 2 4 3 1 0 2 2 R The Venn diagram shows the number of people who like films (F), music (M) and reading (R). (a) Find (i) n (M) , … [1] (ii) n ( R , M ) . … [1] (b) A person is chosen at random from the people who like films. Write down the probability that this person also likes music. … [1] (c) On the Venn diagram, shade M l + (F , R) . [1]

4 marks

Mark scheme: 15 (a) (i) 9 1 (ii) 12 1 5 (b) 1 14 (c) 1

This question in 0580/22 Oct/Nov 2016

20 The diagram shows a fair spinner. 1 6 3 4 3 Anna spins it twice and adds the scores. (a) Complete the table for the total scores. Score on first spin 1 3 3 4 6 1 2 4 4 5 7 3 4 6 6 7 9 Score on 3 4 6 6 7 9 second spin 4 6 [1] (b) Write down the most likely total score. … [1] (c) Find the probability that Anna scores (i) a total less than 6, … [2] (ii) a total of 3. … [1]

5 marks

Mark scheme: 20(a) 5 7 7 8 10 1 7 9 9 10 12 20(b) 7 1 20(c)(i) 7 2FT their 7 or 0.28 or 28% FT 25 25 k B1 for 25 2 6 If zero scored, then SC1 for or if no 5 15 values in the bottom two rows of the table. 20(c)(ii) 0 1FT their 0 FT 25

This question in 0580/21 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 0580/22 May/June 2017

23 (a)  = {students in a class} P = {students who study physics} C = {students who study chemistry} The Venn diagram shows numbers of students. P C 5 11 8 7 (i) Find the number of students who study physics or chemistry. … [1] (ii) Find n P k C l ^ h. … [1] (iii) A student who does not study chemistry is chosen at random. Find the probability that this student does not study physics. … [1] (b) On the Venn diagram below, shade the region D j E l. D E [1]

4 marks

Mark scheme: 23(a)(i) 24 1 23(a)(ii) 5 1

This question in 0580/22 May/June 2017

20 (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) Another box contains 7 black pens and 8 orange pens only. Two pens are chosen at random from this box without replacement. Calculate the probability that at least one orange pen is chosen. … [3]

4 marks

Mark scheme: 20(a) 8 1 oe 15 20(b) 168 3 M2 for oe 210 7 6 7 × 8 1 − × oe or 3( ) oe 15 14 15 × 14 or M1 for 7 6 7 8 8 7 × or × or × oe 15 14 15 14 15 14

This question in 0580/21 May/June 2018

24 Box A and box B each contain blue and green pens only. Raphael picks a pen at random from box A and Paulo picks a pen at random from box B. 2 The probability that Raphael picks a blue pen is . 3 8 The probability that both Raphael and Paulo pick a blue pen is . 15 (a) Find the probability that Paulo picks a blue pen. … [2] (b) Find the probability that both Raphael and Paulo pick a green pen. … [3]

5 marks

Mark scheme: 24(a) 4 2 2 8 oe M1 for × p = or better 5 3 15 24(b) 1 3 4 1 oe 3FT (1 – their ) × correctly evaluated 15 5 3 4 2 M2 for (1 – their ) × (1 – ) oe 5 3 4 2 or M1 for 1 – their or 1 – 5 3

This question in 0580/22 May/June 2018

22 A group of 200 people were asked which city they would like to visit next. The table shows the results. City London Paris New York Tokyo Number of people 50 48 56 46 (a) A person from the group is chosen at random. Write down the probability that this person would like to visit either Paris or Tokyo next. … [2] (b) Two people are chosen at random from the group of 200. Find the probability that one person would like to visit London next and the other person would like to visit New York next. Give your answer as a percentage. … % [3]

5 marks

Mark scheme: 22(a) 94 2 46 48 oe M1 for + oe 200 200 200 22(b) 14.1 or 14.07… 3  50 56  M2 for 2  ×  oe  200 199  50 56 or M1 for × oe 200 199

This question in 0580/21 Oct/Nov 2018

21 (a) In the Venn diagram, shade X l k Y . X Y [1] (b) The Venn diagram below shows information about the number of gardeners who grow melons (M ), potatoes (P ) and carrots (C ). M P 3 6 12 2 5 10 7 23 C (i) A gardener is chosen at random from the gardeners who grow melons. Find the probability that this gardener does not grow carrots. … [2] (ii) Find n ((M k P) j C l) . … [1]

4 marks

Mark scheme: 21(a) 1 X Y 21(b)(i) 9 2 9 k oe B1 for or provided fraction is less 16 k 16 than 1 21(b)(ii) 46 1

This question in 0580/22 May/June 2019

20 (a) 40 children were asked if they have a computer or a phone or both. The Venn diagram shows the results. Have a computer Have a phone 7 8 23 2 (i) A child is chosen at random from the children who have a computer. Write down the probability that this child also has a phone. … [1] (ii) Complete the Venn diagram. Do not have a computer Do not have a phone … … … … [2] (b) In this Venn diagram, shade the region ( A , B l ) + C . A B C [1]

4 marks

Mark scheme: 20(a)(i) 8 1 oe 15 20(a)(ii) 2 B1 for 2 or 3 correct out of 4 regions E Do not have Do not have a computer a phone 23 2 7 8 20(b) E 1 A B C

This question in 0580/23 May/June 2019

4 A bag contains blue, red, yellow and green balls only. A ball is taken from the bag at random. The table shows some information about the probabilities. Colour Blue Red Yellow Green Probability 0.15 0.2 0.43 (a) Complete the table. [2] (b) Abdul takes a ball at random and replaces it in the bag. He does this 200 times. Find how many times he expects to take a red ball. … [1]

3 marks

Mark scheme: 4(a) 0.22 oe 2 M1 for 0.15 + 0.2 + ? + 0.43 = 1 or better 4(b) 40 1

This question in 0580/21 May/June 2020

5 Sofia has a bag containing 8 blue beads and 7 red beads only. She takes one bead out of the bag at random and replaces it. She does this 90 times. Find the number of times she expects to take a red bead. … [2]

2 marks

Mark scheme: 5 42 2 7 M1 for [× 90] 15

This question in 0580/23 May/June 2020

11 A bag contains 7 red discs, 5 green discs and 2 pink discs. (a) 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] (b) Helen adds 9 green discs and some pink discs to the discs already in the bag. The probability of taking a green disc is now 2. 7 Find the number of pink discs that Helen added to the bag. … [2]

4 marks

Mark scheme: 11(a) 50 2 5 M1 for [× 140] 7 + 5 + 2 140 or [× 5] 7 + 5 + 2 11(b) 26 2 5 + 9 2 M1 for = oe n 7 5 + 9 2 or = oe p + 7 + 5 + 2 + 9 7

This question in 0580/23 Oct/Nov 2020

2 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: 2 0.85 oe 1

This question in 0580/21 May/June 2021

71 The probability that Jane wins a game is . 10 (a) Find the probability that Jane does not win the game. … [1] (b) Jane plays this game 50 times. Find the number of times she is expected to win the game. … [1]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 3 1 oe 10 1(b) 35 1

This question in 0580/22 May/June 2021

7 Katy has 5 white flowers, x red flowers and ( 2x + 1) yellow flowers. She picks a flower at random. 1 The probability that it is white is . 12 Find the probability that it is yellow. … [4]

4 marks

Mark scheme: 7 37 4 B3 for x = 18 or 37 [yellow] oe 60 5 or SC2 for answer 12 1 5 or M2 for = oe 12 5 + x + 2 x + 1 or M1 for 5 + x + 2x + 1 oe or [total number of flowers =] 60

This question in 0580/22 Oct/Nov 2021

16 Sachin picks a number at random from the first three multiples of 3. He then picks a number at random from the first three prime numbers. He adds the two numbers to find a score. (a) Complete the table. Multiples of 3 3 9 2 5 11 Prime 3 6 numbers [2] (b) Given that the score is even, find the probability that one of the numbers he picks is 9. … [2]

4 marks

Mark scheme: 16(a) Multiples of 3 2 B1 for at least 4 correct entries + 3 6 9 2 5 8 11 Prime numbers 3 6 9 12 5 8 11 14 16(b) 2 2 their 2 oe B2FT for 5 their 5 their 2 or B1FT for k is any integer in the k range 1 ⩽ k ⩽ 7 c or c is 0, 1 or 2 their 5

This question in 0580/22 Oct/Nov 2021

6 Some cards have either a square, a circle or a triangle drawn on them. Piet chooses one of the cards at random. Complete the table to show the probability of choosing a card with each shape. Shape Square Circle Triangle Probability 0.2 0.32 [2]

2 marks

Mark scheme: 6 0.48 oe 2 M1 for 1   0.2  0.32  oe

This question in 0580/22 May/June 2022

1 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: Question Answer Marks Partial Marks 1 0.95 oe 1

This question in 0580/23 May/June 2022

25 A bag contains 5 red balls, 4 blue balls and 3 green balls. (a) (i) Megan picks a ball at random. Write down the probability that the ball is red or blue. … [1] (ii) Megan replaces the ball. She picks a ball at random, notes the colour and replaces the ball. She repeats this 60 times. Calculate the number of times the ball is expected to be red or blue. … [1] (b) Mick picks 2 of the 12 balls at random, without replacement. Calculate the probability that the balls are different colours. … [4] (c) Marie picks balls at random, without replacement, from the 12 balls. When she picks a green ball she stops. 21 The probability that she picks a green ball on pick n is . 220 Find the value of n. n = … [2]

8 marks

Mark scheme: 25(a)(i) 3 1 oe 4 25(a)(ii) 45 1 FT 60  their (a)(i) correctly evaluated 25(b) 47 4  5 4 4 3 3 2  oe M3 for 1 –   +  +   oe 66  12 11 12 11 12 11   5 4 4 3 3 2  or M2 for   +  +   oe  12 11 12 11 12 11   5 4 5 3 4 3  or   +  +   oe  12 11 12 11 12 11  5 4 5 3 4 3 or M1 for  or  or  or 12 11 12 11 12 11 3 2  oe 12 11 47 If 0 scored, SC1 for oe 72 25(c) 5 2 M1 for correct trial to at least two balls one of which is not green

This question in 0580/21 Oct/Nov 2022

19 Katy picks a number at random from the numbers 2, 3 and 5. She then picks a number at random from the numbers 5, 6, 7 and 9. When she adds the two numbers the answer is even. Find the probability that exactly one of the numbers picked is a 5. … [3]

3 marks

Mark scheme: 19 3 3 M1 for clearly identifying the 7 even oe outcomes 7 2 6, 3 5, 3 7, 3 9, 5 5, 5 7, 5 9 M1 for clearly identifying the 3 even outcomes with just one five 3 5, 5 7 and 5 9 1 If 0 scored SC1 for answer oe 4

This question in 0580/22 Oct/Nov 2022

6 A spinner can land on the colours green, black or red. The table shows the probabilities of the spinner landing on green or black. Colour Green Black Red 2 1 Probability 5 4 (a) Complete the table. [2] (b) Chang spins the spinner 120 times. Find the expected number of times it lands on green. … [1]

3 marks

Mark scheme: 6(a) 7 2  2 1  oe or 0.35 or 35% M1 for 1 –  +  oe 20  5 4  6(b) 48 1

This question in 0580/23 Oct/Nov 2022

5 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: 5 0.22 oe 2 M1 for 1 – (0.3 + 0.35 + 0.13) oe or B1 for 0.78 oe

This question in 0580/21 May/June 2023

5 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: 5 0.4 oe 2 M1 for 1 – (0.2 + 0.05 + 0.35) oe or B1 for 0.6 oe

This question in 0580/22 May/June 2023

7 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: 7(a) 0.11 oe 2 M1 for 1 – (0.3 + 0.16 + 0.18 + 0.25) oe or B1 for 0.89 oe 7(b) 0.46 oe 2 M1 for 0.3 + 0.16

This question in 0580/23 May/June 2023

6 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: 6(a) 0.11 oe 2 M1 for 1 – (0.4 + 0.32 + 0.17) oe 6(b) 576 1

This question in 0580/23 Oct/Nov 2023

5 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. … [1]

3 marks

Mark scheme: 5(a) 54 2 3 360 M1 for 360  oe or 3 oe 20 20 5(b) 17 1 oe 20

This question in 0580/22 Feb/March 2024

12 Farid spins a three-sided spinner with sides labelled A, B and C. The probability that the spinner lands on C is 0.35 . Farid spins the spinner 40 times. Calculate the number of times he expects the spinner to land on C. … [1]

1 marks

Mark scheme: 12 14 1

This question in 0580/22 Feb/March 2024

2 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: 2(a) 0.4 oe 1 2(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 being half their (a)

This question in 0580/21 May/June 2024

23 E F 1 8 6 1 2 3 5 4 S The Venn diagram shows information about the number of students in a class. Some study English (E ), some study French (F ), some study Spanish (S ) and some do not study any of these languages. (a) Find n ( E , F ) l , S ` j. … [1] (b) One student is picked at random from those who study Spanish. Find the probability that this student studies exactly two languages. … [2] Question 24 is printed on the next page.

3 marks

Mark scheme: 23(a) 15 1 23(b) 1 2 oe nfww 2 2  3 4  1 M1 for oe or 1  oe 2 1 3 4 2 1 3 4 with either the numerator or denominator correct

This question in 0580/22 May/June 2024

5 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: 5 0.85 oe 1

This question in 0580/23 May/June 2024

10 Jacinda plays a game with her friend. She can win, lose or draw the game. The probability that she wins the game is 0.28 . (a) Jacinda is twice as likely to draw the game as to lose the game. Work out the probability that she loses the game. … [2] (b) Jacinda plays the game 150 times. Find the expected number of times that she wins. … [1]

3 marks

Mark scheme: 10(a) 0.24 oe 2 M1 for 1 – 0.28 oe 10(b) 42 1

This question in 0580/21 Oct/Nov 2024

16 75 people are asked if they have a car, C, and if they have a job, J. The Venn diagram shows the results. % J C 9 51 13 2 A person is chosen at random from those who have a car. Find the probability that this person also has a job. … [1]

1 marks

Mark scheme: 16 17 1 oe 20

This question in 0580/22 Oct/Nov 2024

8 Pryanka plays a game in which she can win, lose or draw. The table shows the probability of her winning or losing a game. Result of game win lose draw Probability 0.3 0.25 (a) Complete the table. [2] (b) Pryanka plays this game 120 times. Work out the expected number of games she wins. … [1]

3 marks

Mark scheme: 8(a) 0.45 oe 2 M1 for 1 – (0.3 + 0.25) oe 8(b) 36 1

This question in 0580/22 Feb/March 2025

17 (a) A bag contains 6 red marbles, 3 green marbles and 1 blue marble. Two marbles are picked at random from the bag with replacement. Find the probability that both marbles are green. … [2] (b) Another bag contains 4 red counters and 2 yellow counters. Two counters are picked at random from this bag without replacement. (i) Complete the tree diagram. First Second counter counter Red 3 5 Red 4 6 Yellow … Red … 2 6 Yellow Yellow … [2] (ii) Find the probability that one of the two counters is yellow. … [3]

7 marks

Mark scheme: 17(a) 9 2 3 3 oe M1 for  100 10 10 17(b)(i) 2 2 2 B1 for 5 5 4 5 1 5 17(b)(ii) 16 3 3FT their tree diagram dep on probabilities < 1 oe 30 4 2 2 4 M2FT for  +  6 5 6 5 4 2 2 4 or M1FT for  or for  6 5 6 5

This question in 0580/21 May/June 2025

1 The probability of picking a green pen from a box is 0.17 . Find the probability of not picking a green pen from the box. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 0.83 oe 1

This question in 0580/23 May/June 2025

11 Angela picks a number at random from the numbers 1, 2 and 3. She then picks a number at random from the numbers 4, 5 and 6. She adds the two numbers to find the total. (a) Complete the table to show the possible outcomes. First number + 1 2 3 4 5 6 7 Second 5 number 6 [2] (b) Given that the total is odd, find the probability that one of the numbers Angela picks is 3. … [2]

4 marks

Mark scheme: 11(a) 2 B1 for 4 correct First number + 1 2 3 4 5 6 7 Second number 5 6 7 8 6 7 8 9 11(b) 2 2 c oe B1 for answer where c < 5 5 5 2 or seen in working 5

This question in 0580/23 May/June 2025

12 A fitness club has 100 members. 60 swim (S ). 70 cycle (C ). 25 do not swim or cycle. % S C (a) Complete the Venn diagram. [3] (b) One member of the fitness club is chosen at random. For this member, find (i) P(C ) … [1] (ii) P(S + C ) … [1] (iii) P(S , C l). … [1]

6 marks

Mark scheme: 12(a) 3 If values placed: S C B2 for 55 correctly placed OR 5 55 15 B1 for 25 correctly placed M1 for total S = 60 and total C = 70 with intersection not equal zero/not blank 25 OR or Alt method if probabilities placed: B2 for 0.55 oe correctly placed S C OR B1 for 0.25 oe correctly placed 0.05 0.55 0.15 M1 for total S = 0.6 and total C = 0.7 with intersection not equal zero/not blank 0.25 12(b)(i) 70 1 oe 100 12(b)(ii) 55 1 their 55 oe FT from their Venn diagram 100 100 12(b)(iii) 85 1 their 25 + their 5 + their 55 oe FT or 100 100 their 15 1 − from their Venn diagram 100

This question in 0580/22 Oct/Nov 2025

11 Sarah rolls a fair 6-sided dice twice. Find the probability she rolls a number greater than 4 both times. … [2]

2 marks

Mark scheme: 11 1 2 2 2 oe M1 for  oe 9 6 6

This question in 0580/23 Oct/Nov 2025

25 Mahir picks one number at random from the numbers 5, 10 and 15. He then picks one number at random from the numbers 4, 5 and 6. He adds the two numbers. The sample space diagram shows some of the possible outcomes. First number + 5 10 15 4 14 19 Second 5 15 20 number 6 16 21 (a) Complete the sample space diagram. [1] (b) Given that the total of the two numbers is odd, find the probability that one of the numbers added is 15. … [2]

3 marks

Mark scheme: 25(a) 1 9 10 11 25(b) 2 2 their 2 oe FT for 5 their 5 their 2 B1FT for where their 2 ⩽ k ⩽ 9 k c or for where 0 < c ⩽ their 5 their 5

This question in 0580/23 Oct/Nov 2025