O-LevelMathematicsProbability4024/23 · May/June 2025 · Q234 Marks

A box contains 13 pencils. There are 4 red pencils, 7 green pencils and 2 yellow pencils in the box. Two pencils are chosen at random from the box without replacement. Work out the probability that the two pencils are different colours.

Mark scheme

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

[4] 100/156 oe
M3 for 4/13 × 7/12 + 4/13 × 2/12 + 7/13 × 4/12 + 7/13 × 2/12 + 2/13 × 4/12 + 2/13 × 7/12 oe
or M2 for two of [prob pairs]
or M1 for one of [prob pairs]
OR
M3 for 1 - (4/13 × 3/12 + 7/13 × 6/12 + 2/13 × 1/12) oe
or M2 for two of [prob pairs for same colour]
or M1 for one of [prob pairs for same colour]
If 0 scored, SC1 for answer 100/169

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Topic: Probability, O-Level Mathematics (syllabus 4024). Structured question, 4 marks.
Source: O-Level Mathematics, May/June 2025 Paper 2 Variant 3, question 23.

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