# Exam Style Question

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Question id: 133. This question is similar to one that appeared in a GCSE Higher paper in 2015. The use of a calculator is allowed.

### Probability

On the day after one GCSE paper Twitter and the media were buzzing with comments about a particular question about Hanna's sweets. Here is our version:

Hannah has 6 orange sweets and some yellow sweets.

Overall, she has $$n$$ sweets.

The probability of her taking 2 orange sweets is $$\frac13$$.

Prove that: $$n^2-n-90=0$$

Hence or otherwise find $$n$$.

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