9709 P63 - Jun 2012 - Q5
Suzanne has 20 pairs of shoes, some of which have designer labels. She has 6 pairs of high-heeled shoes, of which 2 pairs have designer labels. She has 4 pairs of low-heeled shoes, of which 1 pair has designer labels. The rest of her shoes are pairs of sports shoes. Suzanne has 8 pairs of shoes with designer labels in total.
(i) Copy and complete the table below to show the number of pairs in each category.
| Designer labels | No designer labels | Total |
|---|---|---|
| High-heeled shoes | 6 | |
| Low-heeled shoes | 4 | |
| Sports shoes | ||
| Total | 20 |
Suzanne chooses 1 pair of shoes at random to wear.
(ii) Find the probability that she wears the pair of low-heeled shoes with designer labels.
(iii) Find the probability that she wears a pair of sports shoes.
(iv) Find the probability that she wears a pair of high-heeled shoes, given that she wears a pair of shoes with designer labels.
(v) State with a reason whether the events ‘Suzanne wears a pair of shoes with designer labels’ and ‘Suzanne wears a pair of sports shoes’ are independent.
