A LevelMathsEdexcelStatisticsExam QuestionsProbabilityBasic Probability

Basic Probability (Edexcel A Level Maths: Statistics): Exam Questions

Exam code: 9MA0

3 hours38 questions
Easy
Medium
Hard
Very Hard
1
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1 mark

Magali is studying the mean total cloud cover, in oktas, for Leuchars in 1987 using data from the large data set. The daily mean total cloud cover for all 184 days from the large data set is summarised in the table below.

Daily mean total cloud cover (oktas)

0

1

2

3

4

5

6

7

8

Frequency (number of days)

0

1

4

7

10

30

52

52

28

One of the 184 days is selected at random.

Find the probability that it has a daily mean total cloud cover of 6 or greater.

How did you do?

2
1 mark

In a university 8% of students are members of the university dance club.

Only 40% of the university dance club members can dance the tango.

Find the probability that a student is a member of the university dance club and can dance the tango.

How did you do?

3
2 marks

The heights, in cm, of 100 rockhopper penguins are recorded in the following table:

Height, h (cm)

Frequency

40 \leq h < 45

12

45 \leq h < 50

36

50 \leq h < 55

42

55 \leq h < 60

10

A rockhopper penguin is chosen at random.

Find the probability that the penguin is

(i) at least 50 cm tall

(ii) between 45 and 55 cm tall.

How did you do?

4a
1 mark

A and B are two events such that \text{P}(A) = 0.3, \text{P}(B) = 0.8 and \text{P}(A \text{ and } B) = 0.24.

Determine whether A and B are independent.

How did you do?

4b
1 mark

C and D are two events such that \text{P}(C) = 0.42, \text{P}(D) = 0.51 and \text{P}(C \text{ or } D) = 0.91.

Determine whether C and D are mutually exclusive.

How did you do?

5a
2 marks

A fair spinner has five sections labelled ‘dog’, ‘cat’, ‘dog’, ‘dog’ and ‘rabbit’.

The spinner is spun once. Find the probability the spinner comes to rest on a section labelled

(i) ‘dog’

(ii) ‘rabbit’.

How did you do?

5b
3 marks

The spinner is spun twice.

Find the probability that

(i) the spinner comes to rest on the section labelled ‘cat’ on both spins

(ii) the spinner does not come to rest on a section labelled ‘dog’ on either spin.

How did you do?

6a
1 mark

A tennis club surveys its members about the formats of the sport they participate in. The Venn diagram below shows the probabilities of members of the club participating in two different formats of the sport.

A represents the event that the member participates in the singles competition.

B represents the event that the member participates in the doubles competition.

Venn diagram with sets A, B, and S. A contains 0.46, B contains 0.33, intersection labelled x, area outside both circles in S is 0.1.

Find the value of x.

How did you do?

6b
1 mark

Write down what the probability 0.1 represents in the context of the question.

How did you do?

7a
1 mark

A and B are two events such that \text{P}(A) = 0.25 and \text{P}(B) = 0.7.

Given that A and B are independent, find \text{P}(A \text{ and } B).

How did you do?

7b
1 mark

C and D are two events such that \text{P}(C) = 0.4 and \text{P}(D) = 0.5.

Given that C and D are mutually exclusive, find \text{P}(C \text{ or } D).

How did you do?

8
3 marks

Visitors to a nature museum were polled to see if they liked the museum’s two main attractions — a dinosaur skeleton and a butterfly garden. The probability that a visitor liked the dinosaur skeleton is 0.7. The probability that a visitor liked the butterfly garden is 0.5. The probability a visitor liked both is 0.4.

Draw a Venn diagram to represent this information.

How did you do?

9
4 marks

The lengths, in cm, of 120 adult platypuses are recorded in the following table:

Length, l (cm)

Frequency (female)

Frequency (male)

39 \leq l < 42

14

0

42 \leq l < 45

29

0

45 \leq l < 48

12

7

48 \leq l < 51

6

21

51 \leq l < 54

3

19

54 \leq l < 57

1

5

57 \leq l < 60

0

2

60 \leq l < 63

0

1

One platypus is chosen at random. Find the probability that the platypus

(i) is male

(ii) is less than 51 cm long

(iii) is a male less than 45 cm long

(iv) is a female between 45 cm and 54 cm long.

How did you do?

10
4 marks

Two fair spinners each have three equal sectors numbered 1, 2 and 3. The two spinners are spun together and the product of the numbers indicated on each spinner is recorded.

Find the probability that the product is

(i) exactly 6

(ii) less than 4

(iii) an odd number.

How did you do?

11a
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2 marks

A player draws two cards at random from a shuffled Uno deck. The deck has 108 cards, 8 of which are wild cards. The remaining cards are split evenly between four colours: red, blue, yellow and green.

Find the probability that both cards picked are red.

How did you do?

11b
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2 marks

Find the probability that the player draws exactly one wild card.

How did you do?

1a
2 marks

Three bags, A, B and C, each contain 1 red marble and some green marbles.

  • Bag A contains 1 red marble and 9 green marbles only

  • Bag B contains 1 red marble and 4 green marbles only

  • Bag C contains 1 red marble and 2 green marbles only

Sasha selects at random one marble from bag A.

If he selects a red marble, he stops selecting.

If the marble is green, he continues by selecting at random one marble from bag B.

If he selects a red marble, he stops selecting.

If the marble is green, he continues by selecting at random one marble from bag C.

Draw a tree diagram to represent this information.

How did you do?

1b
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2 marks

Find the probability that Sasha selects 3 green marbles.

How did you do?

1c
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2 marks

Find the probability that Sasha selects at least 1 marble of each colour.

How did you do?

2a
1 mark
Venn diagram with three circles labelled A, B, and C. Overlapping areas show values: A only (0.2), intersection of A and B (0.2), B only (0.1), C (0.2).

The Venn diagram, where p is a probability, shows the 3 events A, B and C with their associated probabilities.

Find the value of p.

How did you do?

2b
1 mark

Write down a pair of mutually exclusive events from A, B and C.

How did you do?

3a
1 mark

The Venn diagram, where p and q are probabilities, shows the three events A, B and C and their associated probabilities.

Venn diagram with three circles A, B, and C. Numbers 0.13 in A, 0.05 in B, 0.3 in C, 0.25 overlapping A and B, dotted labels p, q.

Find straight P open parentheses A close parentheses

How did you do?

3b
3 marks

The events B and C are independent.

Find the value of p and the value of q

How did you do?

4a
1 mark

The Venn diagram shows the probabilities associated with four events, A, B, C and D.

Venn diagram showing four overlapping circles labelled A, B, C, and D with intersecting values 0.07 (for part in B only), 0.24 (for part in A and B but not in C or D), 0.16 (for part in A only, p (for part in B and C but not in A or D), q (for all of D), r (for part in C only) and s (outside of A, B, C and D). Circle D is entirely inside circle A, but doesn't overlap B or C. B overlaps both A and C but not D. A and C are entirely separate from each other.

Write down any pair of mutually exclusive events from A, B, C and D.

How did you do?

4b
1 mark

Given that straight P left parenthesis B right parenthesis equals 0.4, find the value of p.

How did you do?

4c
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2 marks

Given also that A and B are independent, find the value of q.

How did you do?

5a
1 mark

A company has 1825 employees.

The employees are classified as professional, skilled or elementary.

The following table shows

  • the number of employees in each classification

  • the two areas, A or B, where the employees live

bold italic A

bold italic B

Professional

740

380

Skilled

275

90

Elementary

260

80

An employee is chosen at random.

Find the probability that this employee is skilled.

How did you do?

5b
1 mark

An employee is chosen at random.

Find the probability that this employee lives in area B and is not a professional.

How did you do?

5c
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4 marks

Some classifications of employees are more likely to work from home.

  • 65% of professional employees in both area A and area B work from home

  • 40% of skilled employees in both area A and area B work from home

  • 5% of elementary employees in both area A and area B work from home

  • Event F is that the employee is a professional

  • Event H is that the employee works from home

  • Event R is that the employee is from area A

Using this information, complete the Venn diagram below.

Venn diagram with three intersecting circles labelled H, R, and F. Overlapping sections show numbers: 123 (in H and R but not F), 247 (in F and H but not R), 412 (in R only), and 133 (in F only).

How did you do?

6a
3 marks

A college surveys a group of Year 12 students about which of three sports they regularly play. The Venn diagram below shows the probabilities that a randomly selected student plays each sport.

A represents the event that the student plays tennis.

B represents the event that the student plays badminton.

C represents the event that the student plays squash.

q3-medium-3-1-basic-probability-edexcel-a-level-maths-statistics

Given that the probability that a student plays squash is 0.44, find the values of

(i) x

(ii) y.

How did you do?

6b
2 marks

Find the probability that a randomly selected student

(i) plays at least one of the three sports

(ii) plays exactly one of the three sports.

How did you do?

7
4 marks

A and B are two events such that \text{P}(A) = 0.4, \text{P}(B) = 0.8 and \text{P}(A \text{ and } B) = 0.35.

Find

(i) the probability that event B occurs but event A does not occur

(ii) the probability that neither event A nor event B occurs.

How did you do?

8a
3 marks

An ice cream company surveys a group of customers to find out whether they like the company’s two new flavours: chocolate and strawberry. The probability that a customer likes chocolate is 0.2. The probability that a customer likes strawberry is 0.15. The probability that a customer likes neither flavour is 0.68.

Draw a Venn diagram to represent this information.

How did you do?

8b
2 marks

Determine, giving a reason for your answer, whether the events ‘a customer likes chocolate’ and ‘a customer likes strawberry’ are independent.

How did you do?

9a
3 marks

A committee is made up of 13 students and 7 teachers. Two members are selected at random, without replacement, to represent the committee at a meeting.

Draw a tree diagram to represent this selection.

How did you do?

9b
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2 marks

Find the probability that the two members selected are of the same type (i.e. both students or both teachers).

How did you do?

10a
2 marks

A manufacturer tests components using a two-stage quality control process.

  • At stage 1 the probability that a component passes is 0.7.

  • If a component passes stage 1, there is a probability of 0.8 that it is accepted for sale, otherwise it is sent for rework.

  • If a component fails stage 1, there is a probability of 0.2 that it is sent for rework, otherwise it is scrapped.

Draw a tree diagram to represent this information.

How did you do?

10b
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4 marks

Find the probability that a randomly chosen component is

(i) accepted for sale

(ii) sent for rework

(iii) scrapped.

How did you do?

10c
2 marks

Determine, giving a reason for your answer, whether the events ‘passes stage 1’ and ‘sent for rework’ are independent.

How did you do?

11
4 marks

A game is played using a fair spinner with four sectors numbered 1 to 4 and a fair dice with its six sides numbered 1 to 6. The spinner is spun and the dice is rolled, and the score in the game is the positive difference between the two results.

Find the probability that the score in the game is

(i) exactly 0

(ii) 3 or more

(iii) a prime number.

How did you do?

12
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3 marks

A, B, C and D are four events such that \text{P}(A) = 0.28, \text{P}(B) = 0.33, \text{P}(C) = 0.43 and \text{P}(D) = 0.25.

(i) Given that events B and C are mutually exclusive, find \text{P}(B \text{ or } C).

(ii) Given that events A and D are independent, find \text{P}(A \text{ and } D).

How did you do?

13a
3 marks

A burger bar collects data on whether customers order two of its signature items: a burger and a portion of fries. The probability that a customer orders both a burger and fries is 0.12. The probability that a customer orders only one of the two items is 0.71. The probability that a customer orders fries but does not order a burger is 0.03.

Draw a Venn diagram to represent this information.

How did you do?

13b
2 marks

Determine, giving a reason for your answer, whether the events ‘orders a burger’ and ‘orders fries’ are independent.

How did you do?

1a
2 marks

In an after-school club, students can choose to take part in Art, Music, both or neither.

There are 45 students that attend the after-school club. Of these

  • 25 students take part in Art

  • 12 students take part in both Art and Music

  • the number of students that take part in Music is x

Find the range of possible values of x.

How did you do?

1b
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4 marks

One of the 45 students is selected at random.

Event A is the event that the student selected takes part in Art.

Event M is the event that the student selected takes part in Music.

Determine whether or not it is possible for the events A and M to be independent.

How did you do?

2
5 marks

Two bags, A and B, each contain balls which are either red or yellow or green.

Bag A contains 4 red, 3 yellow and n green balls.

Bag B contains 5 red, 3 yellow and 1 green ball.

A ball is selected at random from bag A and placed into bag B.

A ball is then selected at random from bag B and placed into bag A.

The probability that bag A now contains an equal number of red, yellow and green balls is p.

Given that p greater than 0, find the possible values of n and p.

How did you do?

3a
2 marks

The histogram below shows the distribution of masses, in grams, of 80 newly hatched ducklings:

q1-hard-3-1-basic-probability-edexcel-a-level-maths-statistics

Find the probability that a duckling chosen at random has a mass less than 54 g.

How did you do?

3b
2 marks

Estimate the probability that a duckling chosen at random has a mass greater than 53 g.

How did you do?

4a
4 marks

A college surveys a group of Year 12 students about which of three sciences they study. The Venn diagram below shows the probabilities that a randomly chosen student studies each subject.

A represents the event that the student studies biology.

B represents the event that the student studies chemistry.

C represents the event that the student studies physics.

q3-hard-3-1-basic-probability-edexcel-a-level-maths-statistics

The probability that a student studies at least one of the three sciences is 0.92 and the probability that a student studies exactly one of the three sciences is 0.7.

Find the values of x, y and z.

How did you do?

4b
2 marks

Find the probability that a randomly selected student

(i) studies chemistry

(ii) studies exactly two of the three sciences.

How did you do?

5
4 marks

On any given day the probability that Tomás reads poetry is 0.55 and the probability that he visits the pub is 0.75. On every day, he does at least one of these two activities.

Find the probability that on a given day Tomás

(i) both reads poetry and visits the pub

(ii) visits the pub but does not read poetry.

How did you do?

6a
3 marks

A shipment of 20 components contains 12 that are flawless, 7 with a minor defect and 1 with a major defect. Two components are selected at random, without replacement, for inspection.

Draw a tree diagram to represent this selection.

How did you do?

6b
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3 marks

Find the probability that the two components selected are not both of the same type.

How did you do?

7a
4 marks

A customer reports a fault with a product. A technician will attempt up to three times to fix it.

  • On the first attempt, the probability the fix is successful is 0.7.

  • If the first attempt fails, a second attempt is made, with probability 0.6 of success.

  • If the second attempt also fails, a third attempt is made, with probability 0.5 of success.

Each time a fix is successful, there is a probability of 0.2 that the customer accepts a free upgrade (as compensation) and a probability of 0.8 that the fault is simply resolved with no upgrade.

If all three attempts fail, the product is replaced.

Draw a tree diagram to represent this information.

How did you do?

7b
4 marks

Find the probability that

(i) the customer accepts a free upgrade

(ii) the fault is resolved with no upgrade

(iii) the product is replaced.

How did you do?

8a
2 marks

The histogram below shows the distribution of masses, in kg, of 75 newborn calves:

q1-very-hard-3-1-basic-probability-edexcel-a-level-maths-statistics

Find the probability that a calf chosen at random has a mass greater than 21 kg.

How did you do?

8b
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3 marks

Estimate the probability that a calf chosen at random has a mass less than 23.5 kg.

How did you do?

9
4 marks

A, B and C are three events such that \text{P}(A) = 0.28, \text{P}(A \text{ or } C) = 0.4 and \text{P}(B \text{ and } C) = 0.02.

Given that A and C are mutually exclusive, and that B and C are independent, find

(i) \text{P}(C)

(ii) \text{P}(B)

(iii) the probability that event C occurs but event B does not occur.

How did you do?

1a
4 marks

The Venn diagram below shows the probabilities of members of a horror film society having seen various films.

A represents the event that the member has seen Aaaaaaaaaaagh!.

B represents the event that the member has seen Beware the Gloaming.

C represents the event that the member has seen Cute Kittens of Doom.

q3-very-hard-3-1-basic-probability-edexcel-a-level-maths-statistics

Given that half the members of the society have seen Cute Kittens of Doom, and that 38\% of members have seen at least two of the three films, find the values of x, y and z.

How did you do?

1b
3 marks

Find the probability that a randomly selected member of the society

(i) has seen exactly two of the three films

(ii) has seen at least one of the three films but not all three of them.

How did you do?

2
4 marks

A game is played using a fair spinner with four sectors numbered 1 to 4 and a fair eight-sided dice with its sides numbered 1 to 8. The spinner is spun and the dice is rolled, and the score in the game is determined as follows:

  • if the number on the spinner is higher than the number on the dice, the score is the sum of the two numbers

  • if the number on the spinner is lower than the number on the dice, the score is the positive difference of the two numbers

  • if the numbers on the spinner and the dice are equal, the score is the product of the two numbers.

Find the probability that the score in the game is

(i) exactly 7

(ii) 10 or more

(iii) a triangular number (i.e. one of 1, 3, 6, 10, 15, 21, \ldots).

How did you do?

3
5 marks

On any given day the probability that Björn has an avocado with his lunch is 0.39, while the probabilities that he has a bacon butty or a piece of carrot cake are 0.32 and 0.44 respectively. He never has all three items on the same day, but the probability that he has at least one of them is 0.91.

The probability that he has exactly two of the three items is the same regardless of which two items those are.

Find the probability that on a given day Björn has

(i) exactly one of the three items

(ii) a bacon butty but not a piece of carrot cake.

How did you do?

4a
4 marks

A music streaming service collects data about the types of music listened to by its users. The probability that a user listens to pop is 0.25. The probability that a user listens to rock is 0.36. The probability that a user listens to classical is 0.56.

Only 10\% of users listen to none of the three types of music. No user listens to both pop and classical. The probability that a user listens to both rock and classical is twice the probability that a user listens to both pop and rock.

Draw a Venn diagram to represent this information.

How did you do?

4b
3 marks

Determine whether any of the events ‘listens to pop’, ‘listens to rock’ and ‘listens to classical’ are independent of one another.

How did you do?

5a
4 marks

A bag contains 10 black tokens and 6 white tokens. A token is drawn from the bag at random and its colour recorded, and then a fair coin is flipped.

If the coin lands on heads, a second token is drawn from the bag without replacing the first token.

If the coin lands on tails, the first token is replaced in the bag before a second token is drawn.

Draw a tree diagram to represent this experiment.

How did you do?

5b
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2 marks

Find the probability that the second token drawn is white.

How did you do?