Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Suzanne owns 20 pairs of shoes, and some of them have designer labels. She has 6 pairs of high-heeled shoes, and 2 of those pairs have designer labels. She has 4 pairs of low-heeled shoes, and 1 pair of these has a designer label. The remaining pairs are sports shoes. In total, Suzanne has 8 pairs of shoes with designer labels.
(i)[2]

Copy the table below and complete it to show the number of pairs in each category.

(ii)[1]

Find the probability that she wears the pair of low-heeled shoes with designer labels.

(iii)[1]

Find the probability that she wears a pair of sports shoes.

(iv)[1]

Find the probability that she wears a pair of high-heeled shoes, given that she wears a pair of shoes with designer labels.

(v)[2]

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.

(vi)[3]

Find the probability that Suzanne wears a pair of shoes with designer labels on at most 4 days out of the next 7 days.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Just one row or one column of the table is correct.

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