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

Earlier this week this question was in the Edexcel Maths GCSE paper:

There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow.

Hannah takes a random sweet from the bag. She eats the sweet.

Hannah then takes at random another sweet from the bag. She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3.

Show that n² – n – 90 = 0.

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

If you like mathematical puzzles, check-out my new Guardian series Alex Bellos’s Monday Puzzle. I post a new question every two weeks. The next one’s on Monday - and it doesn’t involve sweets.