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A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q59 Marks

A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The random variable X denotes the number of throws required to obtain a pair of tails.

  1. (a)Find the expected value of X.[1]
  2. (b)Find the probability that exactly 3 throws are required to obtain a pair of tails.[1]
  3. (c)Find the probability that fewer than 6 throws are required to obtain a pair of tails.[2]
  4. (d)On a different occasion, a pair of fair coins is thrown 80 times. Use an approximation to find the probability that a pair of tails is obtained more than 25 times.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [B1] 1/(1/4) = 4
  2. [B1] (3/4)^2 * (1/4) (=0.141)
  3. [M1] P(X<6)=1-(3/4)^5
  4. [A1] 0.763
  5. [M1] Mean = 80×0.25= 20
  6. [M1] Var = 80×0.25×0.75 = 15
  7. [M1] P(more than 25) = P(z > (25.5-20)/√15)
  8. [M1] P(z > 1.42)
  9. [M1] 1-0.9222
  10. [A1] 0.0778

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, May/June 2020 Paper 5 Variant 3, question 5.

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