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A-LevelMathematicsProbability and statistics9709/52 · May/June 2024 · Q15 Marks

Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3, independently of other years.

  1. (a)Find the probability that Rajesh is successful for the first time on his 7th attempt.[1]
  2. (b)Find the probability that Rajesh is successful for the first time before his 6th attempt.[2]
  3. (c)Find the probability that Rajesh is successful for the second time on his 10th attempt.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B1] 352947/10000000 or 0.03529... to at least 3sf.
  2. [M1] 1-0.7ᵈ, d = 5, 6.
  3. [A1] Accept 0.83193 to at least 3sf. If M0 scored, SC B1 for 0.8319[3].
  4. [(M1)] 0.3+(0.3)(0.7)+(0.3)(0.7)² + (0.3)(0.7)³ +(0.3)(0.7)⁴[+(0.3)(0.7)⁵]
  5. [(A1)] Accept 0.83193 to at least 3sf. If M0 scored, SC B1 for 0.8319[3].
  6. [M1] (0.7)⁸ × (0.3)² x k, k a positive integer, 1 may be implied. No addition/subtraction/additional terms.
  7. [A1]

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2024 Paper 5 Variant 2, question 1.

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