A-LevelMathematicsProbability and statistics9709/62 · May/June 2025 · Q44 Marks

A biased spinner has four sides. Each side is of a different colour: yellow, red, green or black. The probability, p, that the spinner will land on red is unknown. The spinner was spun 200 times, and the proportion, a, of times that it landed on red was noted. This proportion was used to calculate an approximate 90% confidence interval for p. The width of this confidence interval was 0.1066 correct to 4 significant figures. Find the two possible values of a.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[M1] Allow any z and/or omit '2 ×'. Condone confusion between a and a/200. E.g. 2 x 1.645 x sqrt(a(1-a)/200) = 0.1066
[B1] z = 1.645
[M1] Or for valid attempt to reach quadratic in a by confusing between a and a/(200). E.g. a²-200a + 8398.7 = 0
[A1] a = 0.3(00) 3sf or 0.7(00) 3sf Note: Do not ISW a = 0.3 x 200 or 0.7 x 200 score A0.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2025 Paper 6 Variant 2, question 4.

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