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Question id: 230. This question is similar to one that appeared in a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

Probability

There are $$x$$ left shoes and 7 right shoes in a dark cupboard.

Harper takes at random two shoes from the cupboard.

The probability that Harper takes one left shoe and one right shoe is $$\frac{7}{13}$$

(a) Show that $$x^2-13x+42= 0$$

(b) Find the probability that Harper takes two right shoes.

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