Practice Paper 5 (Probability & Statistics 1) (CIE AS Maths: Pure 2)

Practice Paper Questions

1a
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2 marks

Derek is watching cars pass his window. He knows there's a 25% chance that a passing car will be blue.

Find the probability that the first blue car Derek sees is the 8th car to pass his window.

1b
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2 marks

Find the probability that Derek will see a blue car within the first 8 cars that pass his window.

1c
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1 mark

Find the expected number of cars to pass Derek's window until he sees his first blue car.

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2
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4 marks

The Mythical Creatures Research Centre measures the heights, h , of nine unicorns to the nearest centimetre. The heights are shown below:

            276       219      198       154        213       243       192       161      218

Find the mean and standard deviation of the nine heights.

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3a
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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.

3b
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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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4a
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2 marks

The discrete random variable X has the probability distribution shown in the following table:

 

bold italic x negative 2 0 2 4 6
bold P begin bold style stretchy left parenthesis X equals x stretchy right parenthesis end style p 1 half q begin mathsize 16px style 1 over 15 end style q

It is given that E open parentheses X close parentheses space equals space 0.

Show that p minus 4 q equals 2 over 15.

4b
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1 mark

Write down a second equation involving p and q.

4c
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2 marks

Hence find the values of p and q.

4d
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2 marks

Find Var open parentheses X close parentheses.

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5a
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4 marks

Three letters are chosen at random from the letters in the word REVISION. Find the number of ways that the selection may contain

(i)
no Is
(ii)

exactly one I

(iii)

two Is.

5b
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2 marks

Write down the number of arrangements of three letters chosen at random from the word REVISION that have exactly one letter I.

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6a
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4 marks

Riley is going on holiday and is allowed to bring along four of his toys. At home he has nine different plastic dinosaurs, six different toy cars, and five different wooden reptiles.

How many different selections of his toys can he make if he chooses at least one of each type of toy?

6b
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4 marks

Riley can't decide so he persuades his parents to allow him to bring along five toys instead.

Given that he brings more plastic dinosaurs than any other type of toy, how many different selections can he make now?

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7a
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3 marks

A taxi firm, JustDrive, records data on the amount of time, to the nearest minute, that customers had to wait before their taxis arrived.  A random sample of 20 times is given below:

6 7 16 30 24
27 20 7 5 8
20 24 27 12 34
32 31 6 19 14

        

Find the median and interquartile range of the waiting times.

7b
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3 marks

On the grid, draw a box plot for the information given above.q4b-medium-2-2-data-presentation-edexcel-a-level-maths-statistics

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8
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6 marks

The weight, W kg, of the feed in a sack of pheasant feed produced by a certain manufacturer is modelled as  W tilde N open parentheses table row cell 20 comma end cell cell 1 over 3600 end cell end table close parentheses .

Roger buys twelve sacks of the manufacturer’s pheasant feed to feed to the pheasants who have begun showing up at his backyard bird feeding station.

Find the probability that all twelve sacks contain feed with a weight that is within 35 straight g of 20 kg.

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