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TMUA 2016 · Paper 1 · Question 7 of 20

TMUA 2016 Paper 1 Question 7

Algebra and functions — Two-way classification · working back from a conditional proportion. Try it first; the answer and a full worked solution are below.

TMUA 2016 · Paper 1Algebra and functionsTwo-way classification · working back from a conditional proportion5 options
60% of a sports club's members are women and the remainder are men.

This sports club offers the opportunity to play tennis or cricket. Every member plays exactly one of the two sports.

25 of the male members of the club play cricket;

23 of the cricketing members of the club are women.

What is the probability that a member of the club, chosen at random, is a woman who plays tennis?

  1. A15
  2. B725
  3. C13
  4. D1125
  5. E35
Show the answer and worked solution
answer · B
  1. A15
  2. B725
  3. C13
  4. D1125
  5. E35
Take 100 members: 60 women and 40 men. Male cricketers number 25× 40 = 16. Since 23 of all cricketers are women, men make up 13 of the cricketers, so there are 48 cricketers in all and 32 of them are women. That leaves 60  32 = 28 women playing tennis, a probability of 28100=725. The step people miss is that 16 is one third of the cricket total, not a fraction of the women.