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

Exam code: 9MA0

4 hours39 questions
12 marks

Aand B are two events with  straight P open parentheses A close parentheses equals 0.47 and  straight P open parentheses B close parentheses equals 0.31.  Given that Aand B are independent, write down

(i) straight P open parentheses A vertical line B close parentheses

(ii) straight P open parentheses B apostrophe vertical line A to the power of apostrophe close parentheses

Did this page help you?

21 mark

Aand B are two independent events such that  straight P open parentheses A close parentheses equals 0.3  and straight P open parentheses B close parentheses equals 0.8

Find straight P open parentheses A intersection B close parentheses.

Did this page help you?

3a2 marks

Two events, Aand B are mutually exclusive.

(i) Write down the value of straight P open parentheses A intersection B close parentheses.

(ii) Write down a formula for straight P open parentheses A union B close parentheses in terms of straight P open parentheses A close parentheses and straight P open parentheses B close parentheses.

3b3 marks

Two events, D and E, are such that  straight P open parentheses D close parentheses equals 0.2straight P open parentheses E close parentheses equals 0.4  and  straight P open parentheses E vertical line D close parentheses equals 0.7.

(i) Find  straight P open parentheses D intersection E close parentheses.

(ii) Find  straight P open parentheses D union E close parentheses.

(iii) Find straight P open parentheses D vertical line E close parentheses.

Did this page help you?

42 marks

A and B are two events with straight P open parentheses A close parentheses equals x and  straight P open parentheses B close parentheses equals y,  where x not equal to 0.  Given that A and B are independent, write down the following probabilities in terms of x and y:

(i) straight P open parentheses B vertical line A to the power of apostrophe close parentheses

(ii) straight P open parentheses A intersection B close parentheses

Did this page help you?

5a2 marks

 A and B are two events such that  straight P open parentheses A close parentheses equals 0.4, straight P open parentheses B close parentheses equals 0.7 and  straight P open parentheses A intersection B close parentheses equals 0.2.

Complete the Venn diagram below.

Venn diagram with two overlapping circles labelled A and B, inside a rectangle, illustrating shared and distinct elements of two sets.
5b3 marks

Find

(i) straight P open parentheses A union B close parentheses

(ii) straight P open parentheses A to the power of apostrophe close parentheses

(iii) straight P open parentheses open parentheses A intersection B close parentheses to the power of apostrophe close parentheses

Did this page help you?

6a2 marks

100 children were asked whether they liked football and cricket. 

  • 84 said they liked football. 

  • 58 said they liked cricket. 

  • Of those who did not like football, 10 also said they did not like cricket.

Complete the two-way table illustrating this information.

 

Like football

Does not like football

Total

Like cricket

Does not like cricket

Total

6b3 marks

One of the children is selected at random.

Let F be the event that the child likes football.

Let C be the event that the child likes cricket.

Find

(i) straight P open parentheses C close parentheses

(ii) straight P open parentheses C intersection F close parentheses

(iii) straight P open parentheses C union F close parentheses

Did this page help you?

7a1 mark

Kimona is participating in a snowboarding competition whereby participants are given two attempts to complete a particular trick.  If a participant completes the trick on the first attempt, they are still allowed a second attempt.

From experience the probability of Kimona completing the trick on the first attempt is 0.3.  If Kimona completes the trick on the first attempt, the probability of completing the trick on the second attempt is 0.6.  However, if Kimona does not complete the trick on the first attempt, the probability of completing the trick on the second attempt is 0.5.

Draw a tree diagram to illustrate all the possible outcomes and associated probabilities.

7b3 marks

Find the probability that

(i) Kimona completes the trick on both attempts,

(ii) Kimona completes the trick at least once,

(iii) Kimona does not complete the trick on the second attempt, given that she completes the trick at the first attempt.

Did this page help you?

8a1 mark

The Venn diagram below shows the probabilities associated with three events, U comma space V spaceand W.

Venn diagram with three overlapping circles labelled U, V, W. 0.33 is in U only, 0.07 is in U and V, 0.25 is in V only, 0.08 is in V and W, 0.12 is in W only ad 0.15 is outside the three circles.

Identify a pair of mutually exclusive events.

8b3 marks

Find

(i) straight P open parentheses U union V close parentheses

(ii) straight P open parentheses W to the power of apostrophe close parentheses

(iii) straight P open parentheses U to the power of apostrophe intersection space V to the power of apostrophe close parentheses

8c3 marks

(i) Show that V and W are independent.

(ii) Show that U and Vare not independent.

Did this page help you?

9a2 marks

A box contains 7 blue and 3 red equally sized counters.  A counter is taken from the box and its colour is noted, but it is not replaced in the box.  A second counter is then taken from the box and its colour noted.

Draw a tree diagram to illustrate all the possible outcomes and associated probabilities.

9b3 marks

Find the probability that:

(i) neither counter is blue,

(ii) both counters are the same colour,

(iii) the second counter is blue, given that the first counter is red.

Did this page help you?

1a3 marks

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.

The events B and C are independent.

Find the value of p and the value of q

1b2 marks

Find straight P open parentheses A vertical line B apostrophe close parentheses

Did this page help you?

2a
Sme Calculator
4 marks

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

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).
2b1 mark

Find straight P open parentheses R apostrophe intersection F close parentheses

2c1 mark

Find straight P open parentheses open square brackets H union R close square brackets apostrophe close parentheses

2d
Sme Calculator
2 marks

Find straight P open parentheses F vertical line H close parentheses

Did this page help you?

3a3 marks

A commaBand C are three events with straight P open parentheses A close parentheses equals 0.2straight P open parentheses B close parentheses equals 0.25straight P open parentheses C close parentheses equals 0.6 and straight P open parentheses B intersection C close parentheses equals 0.08.

Events Aand C are mutually exclusive. Events Aand B are independent.

Draw a Venn diagram to illustrate the probabilities.

3b3 marks

Find:

(i) straight P open parentheses A to the power of apostrophe intersection space C to the power of apostrophe close parentheses

(ii) straight P open parentheses open square brackets A apostrophe intersection B close square brackets union C close parentheses

(iii) straight P open parentheses A to the power of apostrophe union open square brackets B intersection C close square brackets to the power of apostrophe close parentheses

Did this page help you?

4a
Sme Calculator
2 marks

240 students are surveyed regarding their belief in supernatural creatures.  144 say they believe in unicorns.  75 say they believe in vampires.  Of those who believe in vampires, 27 also believe in unicorns.

Complete the two-way table to show this information.

Believes in unicorns

Does not believe in unicorn

Total

Believes in vampires

Does not believe in vampire

Total

4b4 marks

One student is chosen at random. 

Let U represent the event that the student believes in unicorns.

Let V represent the event that the student believes in vampires.

Find:

(i) straight P open parentheses U to the power of apostrophe close parentheses

(ii) straight P open parentheses U to the power of apostrophe intersection space V to the power of apostrophe close parentheses

(iii) straight P open parentheses U vertical line V close parentheses

(iv) straight P open parentheses V vertical line U close parentheses

Did this page help you?

5a1 mark

A group of middle and senior school students were asked whether they preferred vinegar or ketchup as a topping on their chips. The following two-way table shows the results of the survey:

 

vinegar

ketchup

total

middle

49

21

70

senior

63

27

90

total

112

48

160

A student is chosen at random.

Let K be the event that the student prefers ketchup.

Let M be the event that the student is in middle school.

Find straight P open parentheses K vertical line M close parentheses.

5b2 marks

Determine whether the events K and M are independent. Give a reason for your answer.

Did this page help you?

63 marks

The following Venn diagram shows the number of adults in a poll who said they enjoy watching action films (A), Bollywood musicals (B), and crime thrillers (C).

Venn diagram with three circles labelled A, B, C showing intersections with numbers: 15 in A only, 16 in B only, 9 in C only, 3 in A and B only, 2 in B and C only, 27 in A and C only, 4 in A, B and C, 23 in none.

One of the adults who was polled is selected at random.  Given that the adult chosen enjoys watching at least one of those three genres of film, find the probability that the adult:

(i) enjoys watching exactly two of the three genres of film,

(ii) does not enjoy watching action musicals.

Did this page help you?

7a4 marks

Three events A comma B and C, are such that B and C are mutually exclusive and A and C are independent. straight P open parentheses A close parentheses equals 0.3straight P open parentheses B close parentheses equals 0.45 and straight P open parentheses C close parentheses equals 0.1.

Given that straight P open parentheses open square brackets A union B union C close square brackets to the power of apostrophe close parentheses equals 0.43, draw a Venn diagram to show the probabilities for events A comma B, and C.

7b
Sme Calculator
5 marks

Find:

(i) straight P open parentheses B vertical line A close parentheses

(ii) straight P open parentheses A vertical line B to the power of apostrophe close parentheses

(iii) straight P open parentheses A vertical line open square brackets B union C close square brackets close parentheses

Did this page help you?

8a
Sme Calculator
3 marks

Given that  straight P open parentheses A close parentheses equals 0.27straight P open parentheses B close parentheses equals 0.39   and  straight P open parentheses A intersection B close parentheses equals 0.21, find:

(i) straight P open parentheses A union B close parentheses

(ii) straight P open parentheses B vertical line A close parentheses

8b
Sme Calculator
2 marks

The event C has  straight P open parentheses C close parentheses equals 0.19. The events A and C are mutually exclusive. 

Given that straight P open parentheses B intersection C close parentheses equals 0.04, find straight P open parentheses A union B union C close parentheses.

Did this page help you?

9a
Sme Calculator
2 marks

A bag contains 15 blue tokens and 27 yellow tokens.  A token is taken from the bag and its colour is recorded, but it is not replaced in the bag.  A second token is then taken from the bag and its colour is recorded.

Draw a tree diagram to represent this information.

9b
Sme Calculator
4 marks

Find the probability that:

(i) the second token selected is blue

(ii) both tokens selected are blue, given that the second token selected is blue. 

Did this page help you?

10a3 marks

Ichabod is a keen chess player who plays one game of chess online every night before going to bed.  In any one of those games, the probabilities of Ichabod winning, drawing, or losing are 0.4, 0.27 and 0.33 respectively.  Following each game, the probabilities of Ichabod sleeping well after winning, drawing or losing are 0.7, 0.9 and 0.2 respectively.

Draw a tree diagram to represent this information.

10b
Sme Calculator
4 marks

Find the probability that on a randomly chosen night

(i) Ichabod loses his chess game and sleeps well

(ii) Ichabod sleeps well.

10c
Sme Calculator
3 marks

Given that Ichabod sleeps well, find the probability that his chess game did not end in a draw.

Did this page help you?

11a2 marks

Some attendees at a pizza fandom convention are surveyed regarding their opinions about anchovies and bananas as pizza toppings. 

  • 144 of them say they do not like anchovies. 

  • 320 of them say they do not like bananas.

  • 28 of them say they like bananas but not anchovies.

  • Only 12 of them like both toppings.

Draw a two-way table to show this information.

11b
Sme Calculator
4 marks

One of the attendees is chosen at random.

Let A be the event that the attendee likes anchovies.

Let B be the event that the attendee likes bananas.

Find:

(i) straight P open parentheses B close parentheses

(ii) straight P open parentheses A to the power of apostrophe intersection B to the power of apostrophe close parentheses

(iii) straight P open parentheses B vertical line A close parentheses

(iv) straight P open parentheses A vertical line B to the power of apostrophe close parentheses

Did this page help you?

1a2 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.

1b
Sme Calculator
2 marks

Given that Sasha selects a red marble, find the probability that he selects it from bag B.

Did this page help you?

2a1 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.

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

2b
Sme Calculator
2 marks

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

2c
Sme Calculator
4 marks

Given further that straight P left parenthesis B to the power of apostrophe vertical line C right parenthesis equals 0.64, find

(i) the value of r,

(ii) the value of s.

Did this page help you?

3a4 marks

A, B  and C are three events with:

  • straight P open parentheses B close parentheses equals 0.3

  • straight P open parentheses A intersection B close parentheses equals 0.01

  • straight P open parentheses B intersection C close parentheses equals 0.12

  • straight P open parentheses open square brackets A union B union C close square brackets to the power of apostrophe close parentheses equals 0.13

Events A and C are mutually exclusive. Events B and C are independent.

Draw a Venn diagram to illustrate the probabilities.

3b3 marks

Find:

(i) straight P open parentheses A intersection B to the power of apostrophe close parentheses

(ii) straight P open parentheses open square brackets A to the power of apostrophe intersection C to the power of apostrophe close square brackets union A close parentheses

(iii) straight P open parentheses open square brackets open square brackets A intersection B to the power of apostrophe close square brackets union open square brackets B to the power of apostrophe intersection C close square brackets close square brackets to the power of apostrophe close parentheses

Did this page help you?

4
Sme Calculator
3 marks

A group of people, aged 18 to 25, and a group of people over 65 years old, were asked whether they would prefer to holiday in Ibiza or Skegness. The following two-way table shows part of the results of the survey:

 

Ibiza

Skegness

total

18-25

 

99

over 65

 

 

45

total

64

80

144

For the people in the sample, age and preferred holiday location are statistically independent.

Find the missing values in the table.

Did this page help you?

5a2 marks

The following Venn diagram shows some of the results for the number of chess players in a poll who said they enjoy playing any, all or none of three chess game openings:

  • the Najdorf Sicilian (N)

  • the Orangutan (O)

  • the Ponziani countergambit (P).

Venn diagram with three overlapping circles labelled N, O, and P.  37 is in N only, 2 is in N and O only, 19 is in O only and 7 is in O and P only.

120 chess players were polled in total, of whom:

  • one half said they enjoy playing the Najdorf Sicilian

  • one third said they enjoy playing the Orangutan

  • one quarter said they enjoy playing the Ponziani countergambit

Use the above information to fill in the missing values in the Venn diagram.

5b2 marks

One of the chess players who was polled is selected at random. 

Find the probability that the chess player enjoys playing:

(i) the Najdorf Sicilian and the Orangutan

(ii) exactly one of the three openings.

5c2 marks

One of the chess players who was polled is selected at random. 

Given that the player enjoys playing at least two of the game openings, find the probability that the player enjoys playing the Ponziani countergambit.

Did this page help you?

6a4 marks

Given that  straight P open parentheses A close parentheses equals 0.34straight P open parentheses A union B close parentheses equals 0.67  and straight P open parentheses A intersection B close parentheses equals 0.02, find:

(i) straight P open parentheses B close parentheses

(ii) straight P open parentheses A vertical line B to the power of apostrophe close parentheses

6b
Sme Calculator
3 marks

The event C has straight P open parentheses C close parentheses equals 0.2. The events B and C are mutually exclusive. 

Given that A and  C are independent, find  straight P open parentheses A union B union C close parentheses.

Did this page help you?

7a
Sme Calculator
3 marks

A bag contains 12 orange marbles, 8 purple marbles and 5 red marbles.  A marble is taken from the bag and its colour is recorded, but it is not replaced in the bag.  A second marble is then taken from the bag and its colour is recorded.

Find the probability that both marbles are different colours.

7b
Sme Calculator
3 marks

Given that both marbles are different colours, find the probability that the second marble is purple.

Did this page help you?

8a3 marks

Rosco is a rural county sheriff who frequently finds himself involved in car chases. During any given car chase, Rosco runs into exactly one of three obstacles; a damaged bridge, an oil slick or a pig pen at the end of a dead-end road.

  • There's a 47% chance that he runs into a damaged bridge.

  • There's a 32% chance that he runs into an oil slick.

If he encounters a damaged bridge, there is a 25% chance that he makes it across safely; otherwise, he lands in the river and ends up covered in mud. 

If he encounters an oil slick, there is a 40% chance that his car spins around, and he will end up continuing his hot pursuit in the wrong direction; otherwise, he goes off the road into a farm pond and ends up covered in mud. 

If he encounters a pig pen at the end of a dead-end road, there is a 15% chance he stops his car in time; otherwise, he drives into the pig pen and ends up covered in mud.

Draw a tree diagram to represent this information.

8b
Sme Calculator
2 marks

Find the probability that, in a randomly chosen car chase, Rosco ends up covered in mud.

8c
Sme Calculator
3 marks

Given that Rosco ends up covered in mud in a randomly chosen car chase, find the probability that he did not encounter an oil slick.

8d
Sme Calculator
2 marks

In the course of a particular day Rosco finds himself engaged in three separate car chases with well-meaning local entrepreneurs.  The car chases may be considered to be independent events.

Find the probability that on that day Rosco does not end up covered in mud.

Did this page help you?

9a
Sme Calculator
4 marks

 Three events, A, B and C, are such that:

  • Aand B are independent

  • Band C are mutually exclusive

  • straight P open parentheses C close parentheses equals 0.55

  • straight P open parentheses open square brackets A intersection B close square brackets union open square brackets A intersection C close square brackets close parentheses equals 0.07

  • 8 cross times straight P open parentheses A close parentheses equals 25 cross times straight P open parentheses B close parentheses

  • straight P open parentheses A to the power of apostrophe intersection C close parentheses equals 10 cross times straight P open parentheses A intersection C close parentheses

Using the above information, draw a Venn diagram to show the probabilities for events A,B and C.

9b
Sme Calculator
4 marks

Find:

(i) straight P open parentheses C vertical line A close parentheses

(ii) straight P open parentheses B vertical line A to the power of apostrophe close parentheses

(iii) straight P open parentheses open square brackets A union B union C close square brackets to the power of apostrophe vertical line open square brackets A union B close square brackets to the power of apostrophe close parentheses

Did this page help you?

1a1 mark

A large college produces three magazines.

One magazine is about green issues, one is about equality and one is about sports.

A student at the college is selected at random and the events G, E and S are defined as follows

G is the event that the student reads the magazine about green issues

E is the event that the student reads the magazine about equality

S is the event that the student reads the magazine about sports

The Venn diagram, where p, q, r and t are probabilities, gives the probability for each subset.

Venn diagram with sets G, E, and S, showing intersections. Values: G=0.08, E=0.09, G and E=0.05, G and S=q, E and S=r, G and E and S=p, outside=0.36.

Find the proportion of students in the college who read exactly one of these magazines.

1b3 marks

No students read all three magazines and straight P left parenthesis G right parenthesis equals 0.25

Find

(i) the value of p

(ii) the value of q

1c4 marks

Given that straight P open parentheses S vertical line E close parentheses equals 5 over 12, find

(i) the value of r

(ii) the value of t

1d3 marks

Determine whether or not the events left parenthesis S intersection E ʹ right parenthesis and G are independent.

Show your working clearly.

Did this page help you?

2a
Sme Calculator
5 marks

A,B and C are three events such that 

  • straight P open parentheses C close parentheses equals 0.37

  • straight P open parentheses A to the power of apostrophe intersection B to the power of apostrophe intersection C close parentheses equals 0.18

  • straight P open parentheses A intersection B intersection C close parentheses equals 0.09

  • straight P open parentheses open square brackets A union B union C close square brackets to the power of apostrophe close parentheses equals 0.21

In addition, the following two relations hold:

  • straight P open parentheses A intersection B intersection C to the power of apostrophe close parentheses space colon space straight P open parentheses A intersection B to the power of apostrophe intersection C close parentheses space colon space straight P open parentheses A to the power of apostrophe intersection B intersection C close parentheses equals 3 colon 4 colon 1

  • straight P open parentheses A close parentheses space colon space straight P open parentheses B close parentheses equals space 9 colon 10

Draw a Venn diagram to illustrate the probabilities.

2b
Sme Calculator
4 marks

Find:

(i) straight P open parentheses A union B to the power of apostrophe union C close parentheses

(ii) straight P open parentheses open square brackets A union C apostrophe close square brackets vertical line open square brackets A union C close square brackets close parentheses

(iii) straight P open parentheses open square brackets B union C close square brackets vertical line open square brackets A union B union C close square brackets union open square brackets A union B union C close square brackets to the power of apostrophe close parentheses

Did this page help you?

3a2 marks

Events Aand B are such that  straight P open parentheses A close parentheses equals 0.23  and  straight P open parentheses B close parentheses equals 0.72.

 Given that straight P open parentheses A to the power of apostrophe intersection B close parentheses equals p, find the range of possible values of  p.

3b1 mark

Additionally, event C is such that straight P open parentheses C close parentheses equals 0.53  and straight P open parentheses A intersection B intersection C close parentheses equals 0.17.

Find the modified range of possible values of p when this additional information is taken into account.

3c3 marks

Given that straight P open parentheses A to the power of apostrophe intersection B intersection C close parentheses equals q, find the range of possible values of q.

Did this page help you?

44 marks

Aand B are events such that 

  • straight P open parentheses A union B close parentheses equals x

  • straight P open parentheses A intersection B to the power of apostrophe close parentheses equals y

  • straight P open parentheses A to the power of apostrophe intersection B close parentheses equals z

where  x greater than z  and  y not equal to 0.

Find the following probabilities in terms of x comma space y spaceand z:

(i) straight P open parentheses A intersection B close parentheses

(ii) straight P open parentheses B vertical line A close parentheses

(iii) straight P open parentheses A vertical line B to the power of apostrophe close parentheses

Did this page help you?

5a
Sme Calculator
4 marks

A bag contains tokens. Each token has an integer from 1 to 15 written on it. For each integer k in the interval 1 less or equal than k less or equal than 15, there are k tokens with the number k written on them. For example:

  • There is one token with a ‘1’ on it,

  • There are two tokens with a ‘2’ on them,

  • There are fifteen tokens with a ‘15’ on them.

A token is taken from the bag and the number on it is recorded, but it is not replaced in the bag.  A second token is then taken from the bag and the number on it is recorded.

Work out the probability that the numbers on the two tokens are neither both prime numbers nor both square numbers.

5b
Sme Calculator
3 marks

Work out the probability that the number on one of the tokens is a prime number, given that the numbers on the two tokens are neither both prime numbers nor both square numbers

5c
Sme Calculator
1 mark

Work out the probability that the number on the first token is a prime number, given that the numbers on the two tokens are neither both prime numbers nor both square numbers

Did this page help you?

6a2 marks

A spinner is labelled with integers from 1 to 5. For each integer k in the interval 1 less or equal than k less than 5, the probability that the spinner lands on k is A k squared, where A is a constant.

Find the value of A.

6b
Sme Calculator
2 marks

Given that the spinner lands on a prime number, find the probability that it lands on an even number.

6c
Sme Calculator
3 marks

The spinner is spun repeatedly. Find the minimum number of times it needs to be spun so that the probability that it lands on a 5 at least once is greater than 0.99.

Did this page help you?

7
Sme Calculator
3 marks

A group of maths students and maths teachers are on a school trip. They have to choose between two activities: reading Latin poetry or partaking in extreme sports. The following incomplete two-way table shows part of the results of the survey:

 

Latin poetry

extreme sports

total

student

63

 

 

teacher

 

 

72

total

 

 

180

For the people in sample, whether each person chooses Latin poetry or extreme sports is statistically independent of whether they are a student or a teacher.

Find the missing values and complete the table of survey results.

Did this page help you?

8a3 marks

Aand B are two events with 

  • straight P open parentheses A intersection B to the power of apostrophe close parentheses equals x

  • straight P open parentheses A intersection B close parentheses equals y

  • straight P open parentheses A to the power of apostrophe intersection B close parentheses equals z

Given that A and B are independent, show that

y squared plus left parenthesis x plus z minus 1 right parenthesis y plus x z equals 0

8b
Sme Calculator
3 marks

In a school:

  • 15% of students like cartoons but do not like love ballads

  • 30% of student like love ballads but do not like cartoons

  • Fewer than 25% of students do not like love ballads and do not like cartoons

Given that whether each student likes cartoons is independent of whether they like love ballads, find the percentage of students who like cartoons and love ballads.

Did this page help you?

9
Sme Calculator
6 marks

A lifestyle magazine for ancient historians recently conducted a poll of its readership.  The following Venn diagram shows some of the results for the numbers of the historians polled who said that they were fans of any, all or none of the following three ancient Near Eastern rulers:

  • the Hittite king Suppiluliuma I (S)

  • the Assyrian king Ashurbanipal (A)

  • the Akkadian king Manishtushu (M).

Venn diagram with circles S, A, and M in a square. Overlapping numbers: only S-35, only A-37, only S&M-40, only S&A-7.

The following information is known.

  • For each historian who was only a fan of Manishtushu, there were 7 who were only fans of Suppiluliuma I.

  • For each two historians who were fans of both Ashurbanipal and Manishtushu but not of Suppiluliuma I, there were nine historians who were fans of all three rulers. 

  • Being a fan of Ashurbanipal and being a fan of Manishtushu were independent events.

  • 180 historians were polled in total. 

One of the historians who was polled is selected at random.  Given that the historian chosen is a fan of at least one of the three rulers, find the probability that the historian is not a fan of Suppiluliuma I.

Did this page help you?

10a3 marks

A crafty coyote spends most of his spare time trying to catch a very fast roadrunner bird.  The coyote’s schemes always involve exactly one of three items:

  • a crate of TNT (with probability 0.51)

  • a large boulder (with probability 0.29)

  • a rocket on wheels.

If the coyote uses a crate of TNT, there is a 95% chance it will explode at the wrong time and injure the coyote while the roadrunner escapes. Otherwise, the coyote is not injured, but the roadrunner still escapes.

If the coyote uses a large boulder, there is an 85% chance it will injure him by landing on his foot while the roadrunner escapes. Otherwise, the coyote is not injured, but the roadrunner still escapes.

If the coyote uses a rocket on wheels, there is a 60% chance he will injure himself by running into a cliff face while the roadrunner escapes. Otherwise, the coyote is not injured, but the roadrunner still escapes.

Draw a tree diagram to represent this information.

10b
Sme Calculator
3 marks

Given that the coyote is injured during one of his schemes, find the probability that his scheme involved a rocket on wheels.

10c
Sme Calculator
3 marks

A wandering statistician informs the coyote that if he tries n of his schemes to capture the roadrunner, then he will have a better than 90% chance of not being injured during at least one of them.

 Find the smallest value of n that makes the statistician’s statement true.

Did this page help you?