A-LevelMathematicsProbability and statistics9709/62 · May/June 2019 · Q14 Marks

Two ordinary fair dice are thrown and the numbers obtained are noted. Event S is 'The sum of the numbers is even'. Event T is 'The sum of the numbers is either less than 6 or a multiple of 4 or both'.

(a)Showing your working, determine whether the events S and T are independent.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] P(S) = ½
[B1] P(T) = 16/36 (4/9)
[M1] P(S∩T) = 10/36 (5/18)
[A1] P(S)P(T) ≠ P(S∩T) so not independent
[B1] P(S) = ½ (Alternative method)
[B1] P(T) = 16/36 (Alternative method)
[M1] P(S∩T) = 10/36 (5/18) (Alternative method)
[A1] Either 18/36, 10/16,P(S) and P(S|T) seen in workings and correct conclusion stated, www Or 16/36, 10/18, P(T) and P(T|S) seen in workings and correct conclusion stated, www (Alternative method)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2019 Paper 6 Variant 2, question 1.

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