A-LevelMathematicsProbability and statistics9709/61 · May/June 2017 · Q25 Marks

Ashfaq throws two fair dice and notes the numbers obtained. R is the event ‘The product of the two numbers is 12'. T is the event ‘One of the numbers is odd and one of the numbers is even'. By finding appropriate probabilities, determine whether events R and T are independent.

Ashfaq throws two fair dice and notes the numbers obtained. R is the event ‘The product of the two numbers is 12'. T is the event ‘One of the numbers is odd and one of the numbers is even'. By finding appropriate probabilities, determine whether events R and T are independent.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] Attempt at P(R) by probability space diag or listing more than half the options, must see a prob, just a list is not enough
[M1] Attempt at P(T) or P(R|T) involving more than half the options
[B1] Value stated, not from P(R) × P(T) e.g. from probability space diagram
[M1] Comparing product values with P(R∩T), or comparing P (R|T) with P(R)
[A1] Correct conclusion must have all probs correct

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2017 Paper 6 Variant 1, question 2.

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