A-LevelMathematicsProbability and statistics9709/52 · May/June 2020 · Q58 Marks

A fair three-sided spinner has sides numbered 1, 2, 3. A fair five-sided spinner has sides numbered 1, 1, 2, 2, 3. Both spinners are spun once. For each spinner, the number on the side on which it lands is noted. The random variable X is the larger of the two numbers if they are different, and their common value if they are the same.

Mark scheme

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

[M1] (Table of outcomes, showing 1, 2, 3 for X, or correctly identifying all outcomes where X=3)
[A1] 7/15 AG
[B1] P(1) or P(2) correct
[B1] 3rd probability correct, FT sum to 1
[B1] x values 1, 2, 3
[B1] E(X) = (1×2 + 2×6 + 3×7)/15 = 35/15 = 7/3
[M1] Var(X) = (1²×2 + 2²×6 + 3²×7)/15 - (7/3)²
[A1] 22/45 (0.489)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, May/June 2020 Paper 5 Variant 2, question 5.

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