A-LevelMathematicsProbability and statistics9709/63 · May/June 2023 · Q23 Marks

A club has 264 members, numbered from 1 to 264. Donash wants to choose a random sample of members for a survey. In order to choose the members for the sample he uses his calculator to generate random digits. His first 20 random digits are as follows. 10612 11801 21473 22759

(a)The numbers of the first two members in the sample are 106 and 121. Write down the numbers of the next two members in the sample.[2]
(b)To obtain the numbers for members after the 4th member, Donash starts with the second random digit, 0, and obtains the numbers 061 and 211. Explain why this method will not produce a random sample.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[1] (a) One correct [180 or 227]. Ignore incorrect numbers.
[1] (a) Both correct [180, 227] and no extra numbers seen. (Allow other correct use of list of digits).
[1] (b) These numbers are not independent of the previous numbers OR Only a finite number of digits used. (Already used these numbers, so therefore not random. Does not include numbers not in the list, therefore not random (not random or biased needs a reason)).

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