A-LevelMathematicsProbability and statistics9709/63 · May/June 2018 · Q36 Marks

The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is x, and the proportion of males who are Beginners is 0.7. The proportion of females who are Advanced swimmers is 0.55. This information is shown in the tree diagram. [Figure 3.1: Tree diagram showing probabilities for gender (Male/Female) and then swimmer classification (Advanced/Beginners).] 0.55 Females Advanced swimmers Beginners X Males 0.70 Advanced swimmers Beginners For a randomly chosen member, the probability of being an Advanced swimmer is the same as the probability of being a Beginner.

(i)Find x.[3]
(ii)Given that a randomly chosen member is an Advanced swimmer, find the probability that the member is male.[3]

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Mark scheme

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

[3] B1 (1-x) and 0.45 (or 0.3) Seen, either on tree diagram or elsewhere
[3] M1 One of the three correct probability equations
[3] A1 Correct answer
[3] M1 'i' x 0.3 as num or denom of a fraction
[3] M1 0.5 (or (1 – ‘i') × 0.55 + ‘i' × 0.3 unsimplified) seen as denom of a fraction
[3] A1 Correct answer

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