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

Practice Paper Questions

1a
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2 marks

A and B are two events such that  P left parenthesis A right parenthesis space equals space 0.35P left parenthesis B right parenthesis space equals space 0.25  and  P left parenthesis A union B right parenthesis equals 0.6.  State, with a reason, whether A and B  are mutually exclusive.

1b
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2 marks

C and D are two events such that  straight P left parenthesis C right parenthesis space equals space 0.2straight P left parenthesis D right parenthesis space equals space 0.4  and straight P left parenthesis C intersection D right parenthesis space equals space 0.18 . State, with a reason, whether C and D  are independent.

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2a
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1 mark

Praewa plays sports every day after school.  She is four times more likely to choose football than tennis and three times more likely to choose basketball than tennis. She does not play any other sport. 

Show that the probability of Praewa choosing tennis is begin mathsize 16px style 1 over 8 end style.

2b
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3 marks

Find the probability that Praewa chooses three different sports on the next three days in a row.

2c
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2 marks

On a five day week chosen at random, find the probability that Praewa chooses football every day.

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3a
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2 marks

In the town of Wooster, Ohio, it is known that 90% of the residents prefer the locally produced Woostershire brand sauce when preparing a Caesar salad.  The other 10% of residents prefer another well-known brand.

30 residents are chosen at random by a pollster.  Let the random variable X represent the number of those 30 residents that prefer Woostershire brand sauce.

Suggest a suitable distribution for X and comment on any necessary assumptions.

3b
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3 marks

Find the probability that

(i)
90% or more of the residents chosen prefer Woostershire brand sauce
(ii)
none of the residents chosen prefer the other well-known brand.
3c
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2 marks

Find

(i)
straight E open parentheses X close parentheses
(ii)
Var open parentheses X close parentheses.

 

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4a
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2 marks

The random variable X has the probability function

straight P open parentheses X equals x close parentheses equals space open curly brackets table attributes columnalign left end attributes row cell 0.23 space space space space space space space space space x equals negative 1 comma 4 end cell row cell k space space space space space space space space space space space space space space space x equals 0 comma 2 end cell row cell 0.13 space space space space space space space space space x equals 1 comma 3 end cell row cell 0 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.

4b
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2 marks

Construct a table giving the probability distribution of X.

4c
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1 mark

Find straight P open parentheses 0 less or equal than X less than 3 close parentheses.

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5a
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8 marks

The random variable  X tilde straight N left parenthesis 13 comma 15 right parenthesis.

Find the value of a, to 3 significant figures, such that:

(i)
straight P left parenthesis X greater than a right parenthesis equals 0.2
(ii)
straight P left parenthesis a less or equal than X less or equal than 14 right parenthesis equals 0.5
(iii)
straight P left parenthesis 13 minus a less or equal than X less or equal than 13 plus a right parenthesis equals 0.9372
5b
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2 marks

Explain why there are no values of a such that space straight P left parenthesis 14 less or equal than X less or equal than a right parenthesis equals 0.5.

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6a
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3 marks

The grouped frequency table below contains information about the lengths of time of Susie’s calls with her customers. The table was used to draw the cumulative frequency curve also shown below.

Time (t minutes) 4 < t ≤8 8 < t ≤ 12 12 < t ≤ 16 16 < t ≤20
Frequency 16 a b c

q4-veryhard-2-2-data-presentation-edexcel-a-level-maths-statistics

Use the graph to find the values of a, b and c.

6b
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3 marks

Use the graph to calculate the interquartile range of times for Susie’s calls.

6c
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2 marks

Use the graph to estimate the percentage of customers whose calls lasted longer than 10 minutes.

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7a
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4 marks

Nine cards are numbered 1, 2, 2, 3, 5, 5, 5, 6 and 8.  

The nine cards are placed randomly in a line. In how many ways can this be done if

(i)

every odd number is separated by an even number

(ii)

all the odd numbers are together?

7b
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6 marks

Four of the nine cards are chosen at random and placed in a line to make a 4-digit code. Find the number of ways the code can be made if

(i)

there are no repeated digits

(ii)

repeated digits are allowed and both 2s are used within the code.

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