A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2021 · Q15 Marks

Each of the 180 students at a college plays exactly one of the piano, the guitar and the drums. The numbers of male and female students who play the piano, the guitar and the drums are given in the following table. Piano Guitar Drums Male 25 44 11 Female 42 38 20 A student at the college is chosen at random.

(a)Find the probability that the student plays the guitar.[1]
(b)Find the probability that the student is male given that the student plays the drums.[2]
(c)Determine whether the events 'the student plays the guitar' and 'the student is female' are independent, justifying your answer.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[B1] 82/180 or 41/90 , 0.456
[M1] Their identified P(M∩D)/P(D) or from data table 11/(20+11), accept unsimplified, condone × 180.
[A1] 11/31 or 0.355 Final answer.
[M1] Their identified P(F) × their identified P(G) or correct seen, can be unsimplified.
[A1] P(F∩G) and P(F)×P(G) seen with correct conclusion, WWW. Values and labels must be seen.

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