Cambridge International AS & A Level
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*7297762714*
MATHEMATICS 9709/51
Paper 5 Probability & Statistics 1 May/June 2020
1 hour 15 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
³ Answer all questions.
³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
³ Write your name, centre number and candidate number in the boxes at the top of the page.
³ Write your answer to each question in the space provided.
³ Do not use an erasable pen or correction fluid.
³ Do not write on any bar codes.
³ If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
³ You should use a calculator where appropriate.
³ You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
³ The total mark for this paper is 50.
³ The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Blank pages are indicated.
JC20 06_9709_51/FP
© UCLES 2020 [Turn over
, 2
1 The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
1.
(a) Show that the probability that the score is 4 is 12 [1]
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The two dice are thrown repeatedly until a score of 4 is obtained. The number of throws taken is
denoted by the random variable X .
(b) Find the mean of X . [1]
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(c) Find the probability that a score of 4 is first obtained on the 6th throw. [1]
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(d) Find P X < 8. [2]
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© UCLES 2020 9709/51/M/J/20
, 3
2 (a) Find the number of different arrangements that can be made from the 9 letters of the word
JEWELLERY in which the three Es are together and the two Ls are together. [2]
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(b) Find the number of different arrangements that can be made from the 9 letters of the word
JEWELLERY in which the two Ls are not next to each other. [4]
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© UCLES 2020 9709/51/M/J/20 [Turn over
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*7297762714*
MATHEMATICS 9709/51
Paper 5 Probability & Statistics 1 May/June 2020
1 hour 15 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
³ Answer all questions.
³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
³ Write your name, centre number and candidate number in the boxes at the top of the page.
³ Write your answer to each question in the space provided.
³ Do not use an erasable pen or correction fluid.
³ Do not write on any bar codes.
³ If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
³ You should use a calculator where appropriate.
³ You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
³ The total mark for this paper is 50.
³ The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Blank pages are indicated.
JC20 06_9709_51/FP
© UCLES 2020 [Turn over
, 2
1 The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
1.
(a) Show that the probability that the score is 4 is 12 [1]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
The two dice are thrown repeatedly until a score of 4 is obtained. The number of throws taken is
denoted by the random variable X .
(b) Find the mean of X . [1]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
(c) Find the probability that a score of 4 is first obtained on the 6th throw. [1]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
(d) Find P X < 8. [2]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
© UCLES 2020 9709/51/M/J/20
, 3
2 (a) Find the number of different arrangements that can be made from the 9 letters of the word
JEWELLERY in which the three Es are together and the two Ls are together. [2]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
(b) Find the number of different arrangements that can be made from the 9 letters of the word
JEWELLERY in which the two Ls are not next to each other. [4]
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
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© UCLES 2020 9709/51/M/J/20 [Turn over
