A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2017 · Q69 Marks

Pack A consists of ten cards numbered 0, 0, 1, 1, 1, 1, 1, 3, 3, 3. Pack B consists of six cards numbered 0, 0, 2, 2, 2, 2. One card is chosen at random from each pack. The random variable X is defined as the sum of the two numbers on the cards.

(i)Show that P(X = 2) = 2/15.[2]
(ii)Draw up the probability distribution table for X.[4]
(iii)Given that X = 3, find the probability that the card chosen from pack A is a 1.[3]

Mark scheme

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

[M1] Mult 2 probs seen (or complete listing of all options) (e.g. 2/10 × 4/6)
[A1] = 2/15 Correct answer legit obtained (AG)
[B1] Correct values for x in table. Any additional values must have P(x)=0 stated
[B1] One correct prob other than P(2) or P(3)
[B1] Correct P(3)
[B1] All correct
[M1] Attempt at P(A=1 AND X=3) as num or denom of a fraction, can be by counting (e.g. 5/10 × 4/6)
[M1] Their P(3) from (ii) as num or denom of a fraction
[A1] = 10/13 (0.769)

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About this question

Topic

Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.

Source

A-Level Mathematics, Feb/Mar 2017 Paper 6 Variant 2, question 6.

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