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A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2022 · Q35 Marks

Three fair 6-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time repeatedly. The score on each throw is the sum of the numbers on the uppermost faces.

  1. (a)Find the probability that a score of 17 or more is first obtained on the 6th throw.[3]
  2. (b)Find the probability that a score of 17 or more is obtained in fewer than 8 throws.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [B1] [P(17 or 18) =] 4/216 = 1/54 , 0.0185(185...) May be seen used in calculation.
  2. [M1] p(1-p)^5, 0 < p < 1
  3. [A1] 0.01686 < p < 0.0169 If A0 scored SC B1 for 0.01686 < p < 0.0169
  4. [M1] 1 - (their (53/54)^7 or 0.98148) or correct), r=7,8 0 < their p < 1
  5. [A1] 0.1225 < p < 0.123

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2022 Paper 5 Variant 2, question 3.

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