How to solve the maths GCSE question about Hannah's sweets that went viral

Students took to Twitter to moan about how difficult the question was.

I agree, there is something inherently comic about the question, since you start off talking about Hannah and sweets and then - BANG - all of a sudden you get a scary-looking equation. 

But READ THE QUESTION. The question is not asking you to solve the equation. It is asking you to do some basic probability.

Let’s solve it:

If Hannah takes a sweet from the bag on her first selection, there is a 6/n chance it will be orange.

That’s because there are 6 oranges and n sweets.

If Hannah takes a sweet from the bag on her second selection, there is a 5/(n-1) chance it will be orange.

That’s because there are only 5 orange sweets left out of a total of n - 1 sweets.

The chance of getting two orange sweets in a row is the first probability MULTIPLIED BY the second one. (That’s the most important thing to learn from your lesson today, peeps!)

Which is 6/n x 5/n–1

The question tells us that the chance of Hannah getting two orange sweets is 1/3.

So: 6/n x 5/n–1 = 1/3

All we need to do now is rearrange this equation.

(6x5)/n(n-1) = 30/(n2 – n) = 1/3

Or 90/(n2 – n) = 1

So (n2 – n) = 90

Voila: n2 – n – 90 = 0

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