A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2020 · Q25 Marks

The probability that a student at a large music college plays in the band is 0.6. For a student who plays in the band, the probability that she also sings in the choir is 0.3. For a student who does not play in the band, the probability that she sings in the choir is x. The probability that a randomly chosen student from the college does not sing in the choir is 0.58.

(a)Find the value of x.[3]
(b)Two students from the college are chosen at random. Find the probability that both students play in the band and both sing in the choir.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] Equation of form 0.6 × a + 0·4 × b = 0·58; a = 0.3, 0.7, b = x, (1 −x)
[B1] Single correct product seen, condone 0.42, in an equation of appropriate form
[A1] x = 0.6
[M1] (Alternative) Equation of form 0.6 x a + 0·4 x b = 0.42; a = 0.3, 0.7, b = x, (1 −x)
[B1] (Alternative) Single correct product seen, condone 0.18, in an equation of appropriate form
[A1] (Alternative) x = 0.6

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