CAIE S1 2012 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2012
SessionJune
TopicHypothesis test of binomial distributions

5 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.
  1. Copy and complete the table below to show the number of pairs in each category.
    Designer labelsNo designer labelsTotal
    High-heeled shoes
    Low-heeled shoes
    Sports shoes
    Total20
    Suzanne chooses 1 pair of shoes at random to wear.
  2. Find the probability that she wears the pair of low-heeled shoes with designer labels.
  3. Find the probability that she wears a pair of sports shoes.
  4. Find the probability that she wears a pair of high-heeled shoes, given that she wears a pair of shoes with designer labels.
  5. 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. Suzanne chooses 1 pair of shoes at random each day.
  6. Find the probability that Suzanne wears a pair of shoes with designer labels on at most 4 days out of the next 7 days.