## Exam-Style Question on Probability## A mathematics exam-style question with a worked solution that can be revealed gradually |

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

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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