A-LevelMathematicsProbability and statistics9709/62 · May/June 2018 · Q26 Marks

In a group of students, ¾ are male. The proportion of male students who like their curry hot is ⅗ and the proportion of female students who like their curry hot is ¼. One student is chosen at random.

(i)Find the probability that the student chosen is either female, or likes their curry hot, or is both female and likes their curry hot.[4]
(ii)Showing your working, determine whether the events 'the student chosen is male' and 'the student chosen likes their curry hot' are independent.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[B1] (i) Seen, accept unsimplified P(M ∩ H) = 3/4 * 3/5 = 9/20 (0.45)
[M1] (i) Numerical attempt at P(F) + P(M ∩ H) = 1/4 + 9/20
[A1] (i) Correct unsimplified expression = 14/20
[A1] (i) Correct final answer = 7/10 (0.7) OE
[M1] (ii) Unsimplified, or better, legitimate numerical attempt at P(M) × P(H) and P(M ∩ H) OR Unsimplified, or better, numerical attempt at P(H) and P(M ∩ H), P(M)
[A1] (ii) Descriptors P(M∩ H) and P(M) × P(H) seen, correct numerical evaluation and comparison, conclusion stated OR Descriptors P(M ∩ H), P(H) and P(M) OR P(M|H) and P(M) seen, numerical evaluation and comparison, conclusion stated

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