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

Practice Paper Questions

1a
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1 mark

Leonardo has constructed a biased spinner with six sectors labelled 0,1, 1, 2, 3 and 5.  The probability of the spinner landing on each of the six sectors is shown in the following table:

number on sector 0 1 1 2 3 5
probability 6 over 20 p 3 over 20 5 over 20 3 over 20 1 over 20


Find the value of p.

1b
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2 marks

Leonardo is playing a game with his biased spinner.  The score for the game, is the number which the spinner lands on after being spun.

Find the probability that Leonardo’s score is

(i)

no more than 1

(ii)

at least 3.

1c
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4 marks
(i)

Find the expected value for Leonardo’s score in a game.

(ii)

Find the standard deviation of Leonardo’s scores.

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2a
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2 marks

How many ways are there to rearrange the ten letters in the word POSITIVITY?

2b
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5 marks

How many ways are there to rearrange the ten letters in the word POSITIVITY if

i)
the three Is must all be together

ii)
the two Ts are not together.

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3a
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2 marks

The random variable  X has the probability function

P open parentheses X equals x close parentheses equals open curly brackets table attributes columnalign left end attributes row cell 0.21 space space space space space space space space space space space space space x equals 0 comma 1 end cell row cell k x space space space space space space space space space space space space space space space space x equals 3 comma 6 end cell row cell 0.11 space space space space space space space space space space space space x equals 10 comma 15 end cell row cell 0 space space space space space space space space space space space space space space space space space otherwise end cell end table close

Find the value of k.

3b
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2 marks

Construct a table giving the probability distribution of X.

3c
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1 mark

Find straight P left parenthesis 3 less than X less or equal than 14 right parenthesis

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4a
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3 marks

A mixed relay team must consist of four competitors two of whom must be male and two of whom must be female. There are nine men and six women trying out for a place on a new team.

During the try-outs the fifteen candidates are split into three groups of four and one group of three. How many ways can this be done if the candidates are divided randomly?

4b
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3 marks

Two of the candidates are brother and sister and have agreed they will only be in the final relay team if they are both successful. How many ways can the final relay team be chosen if the brother and sister are either both in or both out?

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5a
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3 marks

Katin is collecting tadpoles for her biology project. In the pond there are five female tadpoles and six male tadpoles, however they all look the same. She takes two tadpoles at random from the pond, without replacement.

Draw a tree diagram to represent this information.

5b
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3 marks

Find the probability that Katin's two tadpoles are

i)
either both female or both male.

ii)
both female, given that they are the same sex.

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6a
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5 marks

The test scores, X, of a group of RAF recruits in an aptitude test are modelled as a normal distribution with X space tilde space N(210, 27.82).

i)
Find the values of a and b such that space straight P left parenthesis X space less than space a right parenthesis space equals space0.25 and space straight P left parenthesis X space greater than space b right parenthesis space equals space0.25.

ii)
Hence find the interquartile range of the scores.
6b
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3 marks

Those who score in the top 30% on the test move on to the next stage of training.

One of the recruits, Amelia, achieves a score of 231. Determine whether Amelia will move on to the next stage of training.

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7a
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1 mark

The amounts of time engineers spent dealing with individual faults in a power plant were recorded to the nearest minute.  Data on 30 different faults is summarised in the table below.

Time t (minutes) Frequency f
90 - 129 6
130 - 169 8
170 - 199 12
200 - 249 4

Give a reason to support the use of a histogram to represent these data.

7b
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4 marks

On the grid below, draw a histogram to represent the data.q1b-hard-2-2-data-presentation-edexcel-a-level-maths-statistics

7c
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3 marks

Estimate the proportion of individual faults on which engineers spent longer than three hours.

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8
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3 marks

Two fair dice are rolled and the numbers showing on the dice are added together. This is done 18 times and the number of times the sum is not equal to 7 or 11 is recorded.

Define a suitable distribution to model the number of times the sum is not equal to 7 or 11, and justify your choice.

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