A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q13 Marks

There are 300 students at a music college. All students play exactly one of the guitar, the piano or the flute. The numbers of male and female students that play each of the instruments are given in the following table. | | Guitar | Piano | Flute | | :-------------- | :----- | :---- | :---- | | Female students | 62 | 35 | 43 | | Male students | 78 | 40 | 42 |

(i)Find the probability that a randomly chosen student at the college is a male who does not play the piano.[1]
(ii)Determine whether the events 'a randomly chosen student is male' and 'a randomly chosen student does not play the piano' are independent, justifying your answer.[2]

Mark scheme

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

[B1] 120/300 = 0.4 OE
[M1] P(M) × P(P') seen Can be unsimplified but the events must be named in a product
[A1] Numerical comparison and correct conclusion
[M1] P(M|P') or P(P'|M) unsimplified seen with their probs with correctly named events
[A1] Numerical comparison with P(M) or P(P') and correct conclusion

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 3, question 1.

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