Mutually Exclusive Events - Worksheets, Questions and Revision

18 original exam-style questions - 12 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 13)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Statistics

S20 Mutually Exclusive Events

EDEXCEL 1ST0 · Calculator allowed · about 85 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A fair spinner has four coloured sections: red, blue, green and yellow. The table shows the probability that the spinner lands on each colour, but one probability is missing.

Colour	Red	Blue	Green	Yellow
Probability	0.35	0.25	0.15	?

(a)State the rule that connects the probabilities of all the possible outcomes of the spinner.(1)

(b)Work out the probability that the spinner lands on yellow.(2)

(Total for Question 1 is 3 marks)

A bag contains coloured counters. A counter is taken from the bag at random. The table shows the probability of taking each colour of counter.

Colour	Red	Blue	Green
Probability	0.5	0.3	0.2

(a)Write down the probability that the counter is blue.(1)

(b)Write down the colour of counter that is most likely to be taken.(1)

(c)Explain how the table shows that red, blue and green are the only colours of counter in the bag.(1)

(Total for Question 2 is 3 marks)

A box contains coloured pens. The probability that a pen taken at random from the box is each colour is shown in the table.

Colour	Black	Blue	Red	Green
Probability	0.4	0.3	0.2	0.1

(a)Explain why taking a black pen and taking a blue pen are mutually exclusive events.(1)

(b)Work out the probability that the pen taken is black or blue.(2)

(Total for Question 3 is 3 marks)

The probability that it rains in a particular town tomorrow is 0.65.

(a)Work out the probability that it does not rain in the town tomorrow.(2)

(b)State the term used to describe two events, such as 'it rains' and 'it does not rain', that between them cover every possible outcome.(1)

(Total for Question 4 is 3 marks)

Priya rolls a biased six-sided dice a large number of times to estimate the probability of each score. Her estimated probabilities are shown in the table.

Score	1	2	3	4	5	6
Probability	0.1	0.2	0.15	0.25	0.2	0.15

(a)Work out the sum of the six probabilities in the table.(1)

(b)Explain why the table must contain a mistake.(1)

(c)The probability for score 4 was recorded incorrectly. Given that all the other five probabilities are correct, work out the correct probability for score 4.(2)

(Total for Question 5 is 4 marks)

A fair coin is flipped once and, at the same time, a fair four-sided spinner labelled 1 to 4 is spun once. The two-way table shows all 8 equally likely outcomes.

Coin/Spinner	1	2	3	4
Heads	H1	H2	H3	H4
Tails	T1	T2	T3	T4

(a)Write down the probability of getting Heads and a 3 (outcome H3).(1)

(b)Work out the probability of getting (Heads and an even number) or (Tails and a 1). These outcomes are H2, H4 and T1.(2)

(Total for Question 6 is 3 marks)

The spinner shown is divided into 5 equal sections. It is spun once.

(a)Write down P(Red).(1)

(b)Work out P(Red or Blue).(2)

(c)Work out P(not Green).(1)

(Total for Question 7 is 4 marks)

A fair ordinary six-sided dice is rolled once. For each pair of events, state whether they are mutually exclusive or not mutually exclusive, giving a reason.

(i)Event P: rolling a 2. Event Q: rolling a 5.(1)

(ii)Event R: rolling an even number. Event S: rolling a number greater than 4.(1)

(iii)Event T: rolling a number less than 3. Event U: rolling a 6.(1)

(Total for Question 8 is 3 marks)

60 students in Years 10 and 11 each study exactly one of French, Spanish or German. The two-way table shows some of this information.

Year group	French	Spanish	German	Total
Year 10	12	15	a	34
Year 11	10	b	9	26

(a)Work out the value of a.(2)

(b)Work out the value of b.(1)

(c)A student is picked at random from all 60 students. Work out the probability that the student studies German.(2)

(Total for Question 9 is 5 marks)

At a school fete, players pay £1 to spin a biased spinner with three sections: Win, Draw and Lose. P(Win) = 0.3 and P(Draw) = 0.15.

(a)Work out P(Lose).(2)

(b)The spinner is spun 200 times. Work out an estimate for the number of times it lands on Win or Draw.(2)

(Total for Question 10 is 4 marks)

Aaron is planning a survey of the 80 students in his year group to find their favourite sport to play. He designs a questionnaire with four response options: Football, Netball, Athletics, Another sport. Every student must tick exactly one option.

(a)Give a reason why Aaron's four response options should be mutually exclusive and should cover every possible answer (be exhaustive).(1)

(b)Aaron collects these results.

Sport	Football	Netball	Athletics	Another sport
Frequency	28	18	14	?

Work out the missing frequency for 'Another sport'.(2)

(c)Estimate the probability that a student picked at random from the year group prefers Athletics or Another sport.(2)

(Total for Question 11 is 5 marks)

Two fair ordinary six-sided dice are rolled and their scores are added together. The table shows the probability of each possible total, based on the 36 equally likely combinations.

Total	2	3	4	5	6	7	8	9	10	11	12
Probability	1/36	2/36	3/36	4/36	5/36	6/36	5/36	4/36	3/36	2/36	1/36

(a)Write down the probability that the total is 7.(1)

(b)Work out the probability that the total is 7 or 11.(2)

(c)Work out the probability that the total is not 7.(1)

(Total for Question 12 is 4 marks)

In a survey of 40 people, event A is 'owns a cat' and event B is 'owns a dog'. No person in the survey owns both a cat and a dog. The Venn diagram shows the number of people in each region.

(a)Explain why circles A and B do not overlap in the diagram.(1)

(b)Work out the number of people in the survey who own neither a cat nor a dog.(2)

(c)Work out the probability that a person chosen at random from the survey owns a cat or a dog.(2)

(Total for Question 13 is 5 marks)

In the same survey of 40 people, event C is 'recycles regularly' and event D is 'owns a reusable water bottle'. The Venn diagram shows the number of people in each region.

(a)Explain why events C and D are not mutually exclusive.(1)

(b)Write down the number of people who recycle regularly.(1)

(c)Work out the probability that a randomly chosen person owns a reusable water bottle but does not recycle regularly.(2)

(d)Write down the number of people who recycle regularly or own a reusable water bottle (or both).(1)

(Total for Question 14 is 5 marks)

A biased four-sided spinner lands on A, B, C or D. The probability of each outcome is given in terms of x.

Letter	A	B	C	D
Probability	2x	3x	x	4x

(a)Use the fact that the probabilities sum to 1 to write down an equation in x.(1)

(b)Solve your equation to find the value of x.(1)

(c)Work out P(A or D).(2)

(d)Work out P(not B).(1)

(Total for Question 15 is 5 marks)

25 students are asked whether they play Chess and whether they play Checkers. 12 students play Chess, 9 students play Checkers, and 4 students play both games. Complete the Venn diagram, then answer the question below.

(a)Complete the Venn diagram with the number of students in each of the four regions.(3)

(b)Work out the probability that a randomly selected student plays Chess but not Checkers.(1)

(Total for Question 16 is 4 marks)

In a class of 30 students, event E is 'studies French' and event F is 'studies Art'. 18 students study French, 14 study Art, and 7 study both French and Art. For events that are not mutually exclusive, P(E or F) = P(E) + P(F) - P(E and F).

(a)Work out the number of students who study French or Art (or both).(2)

(b)Hence write down the probability that a randomly chosen student studies French or Art.(1)

(c)Work out the number of students who study neither French nor Art.(2)

(Total for Question 17 is 5 marks)

A newspaper claims: 'In our reader survey, 55% of readers said they read the Sport section and 60% said they read the Business section, so at least 15% of readers must read both sections.'

(a)Explain why the events 'reads Sport' and 'reads Business' cannot be mutually exclusive.(2)

(b)Show that at least 15% of readers must read both sections.(2)

(Total for Question 18 is 4 marks)

Mark scheme · S20 Mutually Exclusive Events

Question 1

(a) B1 the probabilities of all the possible outcomes sum to 1 (oe)
(a) Answer: The probabilities of all the possible outcomes sum to 1.
(b) M1 0.35 + 0.25 + 0.15 (= 0.75), oe
(b) A1 0.25 cao
(b) Answer: 0.25

Question 2

(a) B1 0.3 cao
(a) Answer: 0.3
(b) B1 Red cao
(b) Answer: Red
(c) B1 0.5 + 0.3 + 0.2 = 1, so these outcomes are exhaustive (oe)
(c) Answer: 0.5 + 0.3 + 0.2 = 1, so red, blue and green must be all of the possible outcomes.

Question 3

(a) B1 a single pen cannot be both black and blue, so the two events cannot happen at the same time (oe)
(a) Answer: A pen cannot be both black and blue at the same time, so the events cannot both happen.
(b) M1 0.4 + 0.3, oe
(b) A1 0.7 cao
(b) Answer: 0.7

Question 4

(a) M1 1 - 0.65, oe
(a) A1 0.35 cao
(a) Answer: 0.35
(b) B1 exhaustive (events) cao
(b) Answer: Exhaustive

Question 5

(a) B1 1.05 cao
(a) Answer: 1.05
(b) B1 the probabilities of all the outcomes should sum to 1, but they sum to 1.05 (oe)
(b) Answer: The probabilities should add up to 1, but they add up to 1.05, which is too high.
(c) M1 0.1+0.2+0.15+0.2+0.15 (= 0.8), oe
(c) A1 0.2 cao
(c) Answer: 0.2

Question 6

(a) B1 1/8 oe (0.125)
(a) Answer: 1/8
(b) M1 identifying the 3 outcomes H2, H4, T1 from the 8 in the table, oe
(b) A1 3/8 cao
(b) Answer: 3/8

Question 7

(a) B1 2/5 oe (0.4)
(a) Answer: 2/5
(b) M1 2/5 + 1/5, oe
(b) A1 3/5 cao
(b) Answer: 3/5
(c) B1 4/5 oe (1 - 1/5)
(c) Answer: 4/5

Question 8

(i) B1 mutually exclusive - a single roll cannot score both 2 and 5 (oe)
(i) Answer: Mutually exclusive
(ii) B1 not mutually exclusive - 6 is even and greater than 4, so R and S can both happen (oe)
(ii) Answer: Not mutually exclusive
(iii) B1 mutually exclusive - the score cannot be less than 3 and equal to 6 (oe)
(iii) Answer: Mutually exclusive

Question 9

(a) M1 34 - 12 - 15, oe
(a) A1 7 cao
(a) Answer: 7
(b) B1 7 cao
(b) Answer: 7
(c) M1 (a + 9)/60 = (7+9)/60, oe ft
(c) A1 4/15 oe cao
(c) Answer: 4/15

Question 10

(a) M1 1 - 0.3 - 0.15, oe
(a) A1 0.55 cao
(a) Answer: 0.55
(b) M1 (0.3+0.15) x 200, oe
(b) A1 90 cao
(b) Answer: 90

Question 11

(a) B1 so that every student can choose exactly one option, making the results easy to collect and process (oe)
(a) Answer: If the options overlapped or missed a possibility, some students could tick more than one box or none, and the results would be hard to process.
(b) M1 80 - 28 - 18 - 14, oe
(b) A1 20 cao
(b) Answer: 20
(c) M1 (14+20)/80, oe ft
(c) A1 17/40 oe cao
(c) Answer: 17/40

Question 12

(a) B1 6/36 oe (1/6)
(a) Answer: 1/6
(b) M1 6/36 + 2/36, oe
(b) A1 2/9 oe cao
(b) Answer: 2/9
(c) B1 5/6 oe ft (1 - 6/36)
(c) Answer: 5/6

Question 13

(a) B1 no person owns both a cat and a dog, so A and B are mutually exclusive (oe)
(a) Answer: A and B are mutually exclusive - nobody in the survey owns both a cat and a dog.
(b) M1 40 - 14 - 11, oe
(b) A1 15 cao
(b) Answer: 15
(c) M1 (14+11)/40, oe
(c) A1 5/8 oe cao
(c) Answer: 5/8

Question 14

(a) B1 it is possible to belong to both C and D at the same time - 6 people do both (oe)
(a) Answer: C and D are not mutually exclusive because 6 people both recycle and own a reusable bottle.
(b) B1 15 cao
(b) Answer: 15
(c) M1 identifying the 'only D' region = 13, oe
(c) A1 13/40 oe cao
(c) Answer: 13/40
(d) B1 28 cao
(d) Answer: 28

Question 15

(a) B1 2x+3x+x+4x = 1 oe (10x = 1)
(a) Answer: 10x = 1
(b) B1 0.1 cao ft
(b) Answer: 0.1
(c) M1 2x+4x = 6x, oe ft
(c) A1 0.6 oe cao ft
(c) Answer: 0.6
(d) B1 0.7 oe cao ft
(d) Answer: 0.7

Question 16

(a) B1 8 correctly placed in the 'Chess only' region (12-4)
(a) B1 5 correctly placed in the 'Checkers only' region (9-4) and 4 in the overlap
(a) B1 8 correctly placed outside both circles (25-8-5-4)
(a) Answer: Chess only: 8, Checkers only: 5, both: 4, neither: 8.
(b) B1 8/25 oe ft
(b) Answer: 8/25

Question 17

(a) M1 18+14-7, oe
(a) A1 25 cao
(a) Answer: 25
(b) B1 5/6 oe ft (25/30)
(b) Answer: 5/6
(c) M1 30-25, oe ft
(c) A1 5 cao ft
(c) Answer: 5

Question 18

(a) M1 if mutually exclusive, P(Sport or Business) = 55%+60% = 115% (oe)
(a) A1 115% is more than 100%, which is impossible, so some readers must read both (oe)
(a) Answer: If the events were mutually exclusive, P(Sport or Business) would be 55%+60%=115%, which is impossible since probabilities cannot exceed 100%. So some readers must read both.
(b) M1 P(Sport or Business) is at most 100%, so P(both) is at least 55%+60%-100%, oe
(b) A1 15% correctly shown with a concluding statement
(b) Answer: At least 15% read both sections.

Mark my answers

Mutually Exclusive Events - Worksheets, Questions and Revision

More on this topic

Next in this strand

S20 Mutually Exclusive Events

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18