OCR A Level Maths: Statistics

Topic Questions

3.2 Further Probability (A Level only)

1a
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3 marks

Write the following probability statements in words.
The first one has been done for you.

(i)
straight P open parentheses straight A intersection straight B close parentheses " The probability that A has happened and B  has happened.”

(ii)
straight P open parentheses straight A union space straight B close parentheses

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

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

 

1b
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3 marks

For each of the probability statements from part (a), including part (i), draw a Venn diagram and use shading to illustrate the probability.
(You may assume that and  are not mutually exclusive.)

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2a
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2 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  P open parentheses A intersection B close parentheses equals 0.2.

 Complete the two missing probabilities in the Venn diagram below.q2-easy-3-2-further-probability-edexcel-a-level-maths-statistics-1

2b
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3 marks

Use the Venn diagram, or otherwise, to 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

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3a
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2 marks

100 children were asked whether they liked football and cricket.  84 said they liked football (F).  58 said they liked cricket (C).  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 (bold F) Dislike Football (bold F to the power of apostrophe) Total
Like Cricket (C)     58
Dislike Cricket (C’)   10  
Total 84   100

3b
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3 marks

One of the children is selected at random. Find the probability that

(i)
they like cricket

(ii)
they like both football and cricket

(iii)
they like football or cricket, but not both.

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4a
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2 marks

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

(i)
Complete this formula for independent events: straight P open parentheses A intersection B close parentheses space equals long dash cross times straight P open parentheses straight B close parentheses

(ii)
Use the formula to find straight P open parentheses A intersection B close parentheses.
4b
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3 marks

Another formula for independent events is straight P open parentheses A intersection B close parentheses space equals space straight P open parentheses straight A close parentheses space cross times straight P open parentheses straight B vertical line straight A close parentheses   where  straight P open parentheses B vertical line A close parentheses  means the probability of B happening given that A has already happened.

 (i)      Use the formula to find straight P open parentheses B vertical line A close parentheses

(ii)
Deduce a similar formula involving straight P open parentheses A vertical line B close parentheses  and use it to find  text P end text open parentheses A vertical line B close parentheses.
4c
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1 mark

Briefly explain why, for independent events Aand Bstraight P open parentheses A vertical line B close parentheses equals straight P open parentheses straight A close parentheses .

 

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5a
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2 marks

Kimona is participating in a snowboarding competition whereby participants are given two attempts to complete a particular trick.  If a participant completes the trick at the first attempt, they are still allowed a second attempt.
From experience the probability of Kimona completing the trick at the first attempt is 0.3  If Kimona completes the trick at the first attempt, the probability of completing the trick at the second attempt is 0.6.  However, if Kimona fails at the first attempt, the probability of completing the trick at the second attempt is 0.5.

 Complete the tree diagram below representing Kimona’s situation.
(C denotes a completed trick, F denotes a failed trick.)q5a-easy-3-2-further-probability-edexcel-a-level-maths-statistics

5b
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2 marks

Use the tree diagram to find the probability that

(i)      Kimona fails both attempts at completing the trick

(ii)     Kimona completes the trick at least once.

 

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6a
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2 marks

Two events, Aand B are mutually exclusive.

(i)
Briefly explain why straight P open parentheses A intersection B close parentheses equals 0.

(ii)
Hence use the formula straight P open parentheses A union B close parentheses space equals straight P open parentheses straight A close parentheses plus straight P open parentheses straight B close parentheses minus straight P open parentheses straight A intersection straight B close parentheses to show that, for mutually exclusive events, straight P open parentheses A union B close parentheses equals straight P open parentheses straight A close parentheses plus straight P open parentheses straight B close parentheses.
6b
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3 marks

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

(i)
Use the formula  straight P open parentheses D intersection E close parentheses equals straight P open parentheses D close parentheses cross times straight P open parentheses E vertical line D close parentheses  to find  straight P open parentheses D intersection E close parentheses.

(ii)
Use the formula P open parentheses D intersection E close parentheses equals P open parentheses D close parentheses plus P open parentheses E close parentheses minus P open parentheses D union E close parentheses to find  straight P open parentheses D space U space E close parentheses.

(iii)
Use the formula  P open parentheses D intersection E close parentheses equals P open parentheses D close parentheses cross times P open parentheses E close parentheses  to deduce whether the events D and E are independent or not.

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7a
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1 mark

The Venn diagram below shows the probabilities associated with three events, U comma space V spaceand W.q7-easy-3-2-further-probability-edexcel-a-level-maths-statistics

Explain how the Venn diagram shows that events U are W mutually exclusive.

7b
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3 marks

Use the Venn diagram to 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)
P open parentheses U to the power of apostrophe intersection space V to the power of apostrophe close parentheses
7c
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4 marks
(i)
Find   straight P open parentheses U close parentheses, straight P open parentheses V close parentheses and straight P open parentheses W close parentheses

(ii)
Use the general formula P open parentheses A intersection B close parentheses equals P open parentheses A close parentheses cross times P open parentheses B close parentheses to show that V and W are independent but U and Vare not.

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8a
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3 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 represent this information.

 

8b
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2 marks

Use your tree diagram from part (a) to find the probability that:

(i)
both counters are of the same colour

(ii)
neither counter is blue.
8c
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1 mark

Explain why, if four counters were taken one at a time and without replacement, the probability of all of them being red is zero.

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1a
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4 marks

A,B  and C are three events with  straight P open parentheses B close parentheses equals 0.3straight P open parentheses A intersection B close parentheses equals 0.01P open parentheses B intersection C close parentheses equals 0.12 and  straight P open parentheses open parentheses A union B union C close parentheses to the power of apostrophe close parentheses equals 0.13 .

Given that events A and C are mutually exclusive, and that events and C are independent, draw a Venn diagram to illustrate the probabilities.

1b
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3 marks

Find:

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

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

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

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2a
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2 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.

Let A and B be the events ‘likes anchovies as a pizza topping’ and ‘likes bananas as a pizza topping’ respectively.

 Draw a two-way table to show this information.

2b
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4 marks

One of the attendees is chosen at random. 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

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3a
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3 marks

A and B are two events with straight P open parentheses A close parentheses space equalsx  and  straight P open parentheses B close parentheses equalsy,  where xnot equal to0.  Given that A and B are independent, find 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 vertical line A close parentheses

 

3b
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4 marks

A group of 18- to 25-year-olds, 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

(i)

Find P(over 65) and P(Ibiza)

(ii)

Given that for the people in the sample the events ‘is over 65’ and ‘prefers to holiday in Ibiza’ are independent, find the missing values and complete the table of survey results.

 

 

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4a
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2 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), and the Ponziani countergambit (P).q4-hard-3-2-further-probability-edexcel-a-level-maths-statistics

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, and one fourth said they enjoy playing the Ponziani countergambit. 

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

4b
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3 marks

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

Given that the chess player chosen enjoys playing at least one of the three openings, find the probability that the chess player enjoys playing:

(i)
the Orangutan

(ii)
only one of the three openings

(iii)
at least two of the three openings

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5a
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5 marks

 Three events,A, B and C, are such that Aand B are independent Band C and  are mutually exclusive. straight P open parentheses C close parentheses equals 0.55P open parentheses open parentheses A intersection B close parentheses union open parentheses A intersection C close parentheses close parentheses equals 0.07, and the following two relations also hold: 

8 space straight P open parentheses A close parentheses equals 25 space straight P open parentheses B close parentheses

straight P open parentheses A to the power of apostrophe intersection C close parentheses equals 10 space 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.

 

5b
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3 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 parentheses A union B union C close parentheses to the power of apostrophe vertical line open parentheses A union B close parentheses to the power of apostrophe close parentheses

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6a
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4 marks

Given that  straight P open parentheses A close parentheses equals 0.34P 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
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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  P open parentheses A union B union C close parentheses.

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7a
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4 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.

Draw a tree diagram to represent this information.

7b
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4 marks

Find the probability that:

(i)
both marbles are different colours

(ii)
the second marble is purple, given that both marbles are different colours.

 

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8a
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3 marks

Rosco is a somewhat inept rural county sheriff who frequently finds himself involved in car chases with well-meaning local entrepreneurs.  During any given car chase, Rosco inevitably runs into one of three obstacles – a damaged bridge (with probability 0.47), an oil slick (with probability 0.32), or a pigpen at the end of a dead-end road.

If he encounters a damaged bridge there is a 25% chance that he will make 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 will spin 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 pigpen at the end of a dead-end road there is a 15% chance he will stop his car in time; otherwise he drives into the muddy end of the pigpen while the pigs sit at the other end laughing.  If he drives into the muddy end of a pigpen there is a 20% chance he will only end up covered in mud; otherwise he ends up covered in mud and other things that are found in pigpens.

Draw a tree diagram to represent this information.

8b
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3 marks

Find the probability that in the course of a randomly chosen car chase

(i)
Rosco ends up covered in mud

(ii)
Rosco ends up covered in mud, but only in mud.
8c
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3 marks

Given that Rosco ends up covered in mud in the course of a randomly chosen car chase, find the probability that he didn’t encounter an oil slick. Give your answer as an exact value.

8d
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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.

Determine the probability that on that day Rosco will not end up covered in other things that are found in pigpens.

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1a
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4 marks

A commaBand C are three events with straight P open parentheses A close parentheses = 0.2, straight P open parentheses B close parentheses space 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.   .

Given that events Aand C are mutually exclusive, and that events Aand B are independent, draw a Venn diagram to illustrate the probabilities.

1b
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3 marks

Find:

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

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

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

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2a
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2 marks

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

Draw a two-way table to show this information.

2b
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4 marks

One student is chosen at random.  Find:

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

(ii)
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

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3a
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2 marks

Aand B are two events with  straight P open parentheses A close parentheses space equals space 0.47 and  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)
P open parentheses B vertical line A to the power of apostrophe close parentheses
3b
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4 marks

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

(i)

Find and P(ketchup|middle) and P(middle|ketchup).

(ii)
Use your results from part (b)(i) to show that for the students in the sample ‘is in middle school’ and ‘prefers ketchup on chips’ are independent events.

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4
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3 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).q4-medium-3-2-further-probability-edexcel-a-level-maths-statistics

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 enjoys watching:

(i)
Bollywood musicals

(ii)
only one of the three genres of film

(iii)
exactly two of the three genres of film.

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5a
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4 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 0.3P open parentheses B close parentheses equals 0.45   and  straight P open parentheses C close parentheses equals 0.1.

Given that P open parentheses open parentheses A union B union C close parentheses 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.

 

5b
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3 marks

Find:

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

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

(iii)
P open parentheses A vertical line open parentheses B U C close parentheses close parentheses

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6a
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4 marks

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

(i)
P open parentheses A union B close parentheses

(ii)
P open parentheses B vertical line A close parentheses
6b
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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 P open parentheses A union B union C close parentheses.

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7a
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3 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.

7b
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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. 

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8a
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3 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.

8b
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4 marks

Find the probability that on a randomly chosen night

(i)
Ichabod loses his chess game and sleeps well

(ii)
Ichabod sleeps well.
8c
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4 marks

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

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1a
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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 comma straight P open parentheses A intersection B intersection C close parentheses equals 0.09 and straight P open parentheses open parentheses A union B union C close parentheses 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.

1b
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4 marks

Find:

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

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

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

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2a
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1 mark

The discrete random variable has probability function

P open parentheses X equals x close parentheses equals k x squared comma spacex =1,2,3,4,5

Find the value of k.

2b
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3 marks

Draw a two-way table of probabilities for the events ‘is odd’ (O) and ‘is prime’ (P).

2c
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3 marks

Find:

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

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

(iii)
straight P open parentheses P vertical line O close parentheses

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3a
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3 marks

Aand B are two events with  P open parentheses A intersection B to the power of apostrophe close parentheses equals x comma P open parentheses A intersection B close parentheses equals y and  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

3b
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4 marks

A group of maths students and maths teachers were asked whether they preferred reading Latin poetry or partaking in extreme sports during their free time. The following two-way table shows part of the results of the survey:

  Latin poetry extreme sports total
student 63    
teacher     72
total     180


Given that for the teachers and students in the sample the events ‘is a maths student’ and ‘prefers to read Latin poetry during free time’ are independent, find the missing values and complete the table of survey results.

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4
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8 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), and the Akkadian king Manishtushu (M).q4-very-hard-3-2-further-probability-edexcel-a-level-maths-statistics

180 historians were polled in total.  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.  Most of the historians were, as expected, fans of at least one of the three rulers, but it was also discovered that being a fan of Ashurbanipal and being a fan of Manishtushu were independent events.

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 exact probability that the historian is a fan of: 

(i)
Suppiluliuma I

(ii)
at least two the three rulers

(iii)
exactly two of the three rulers.

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5a
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3 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 P open parentheses A to the power of apostrophe intersection B close parentheses equals p, find the range of possible values of  p.

 

5b
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2 marks

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

Determine whether this additional information would change your answer to part (a), and if it would then give the modified range of possible values of p when this additional information is taken into account.

5c
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3 marks

Given that 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.

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6
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4 marks

Aand B are events such that  P open parentheses A union B close parentheses equals xP open parentheses A intersection B to the power of apostrophe close parentheses equals y and P open parentheses A to the power of apostrophe intersection B close parentheses equals z,  where  x not equal to 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)
P open parentheses B vertical line A close parentheses

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

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7
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7 marks

A bag contains tokens that each have a single number written on them.  The integers between 1 and 15 are all represented on the tokens.  There is one token with a ‘1’ on it, two tokens with a ‘2’ on them, and so on, up until 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.

Using a tree diagram, or otherwise, work out the probabilities of the following events:

(i)
the numbers on the two tokens are neither both prime numbers nor both square numbers

(ii)
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

(iii)
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

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8a
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3 marks

A crafty coyote spends most of his spare time trying to catch a very fast roadrunner bird.  The coyote’s schemes always involve one of three items procured from a well-known mail order retailer – a crate of TNT (with probability 0.51), a large boulder (with probability 0.29), or 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 it will simply not explode at all and the roadrunner will escape.  If the coyote uses a large boulder there is an 85% chance it will injure him by landing on his head while the roadrunner escapes; otherwise it will injure the coyote by landing on his foot while the roadrunner 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 roadrunner will escape after tricking the coyote into riding the rocket off the top of a cliff.   If the coyote rides the rocket off the top of a cliff he will either get injured when the rocket explodes in mid-air, or get injured by crashing into a mountain on the other side of the valley, or land safely on the ground after his parachute unexpectedly functions properly.  It is twice as likely that the rocket will explode as it is that the coyote will crash into a mountain, and five times as likely that the coyote will crash into a mountain as it is that he will land safely using his parachute.

Draw a tree diagram to represent this information.

8b
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5 marks
(i)
Given that the coyote is injured during one of his schemes, find the exact probability that he is not injured by an explosion.

(ii)
Given that the coyote is not injured during one of his schemes, find the exact probability that his scheme involved a rocket on wheels.
8c
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3 marks

A wandering statistician informs the coyote that if he undertakes n of his schemes to capture the roadrunner, then he will have a better than 50% chance of not being injured during at least one of them.

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

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