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?
- A15
- B725
- C13
- D1125
- E35
Show the answer and worked solution
answer · B
- A15
- B725
- C13
- D1125
- 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.