Hannah's sweets: the solution to THAT super-hard GCSE maths question

Come on, Hannah. Why not just try the yellow sweets? 


The Student Room has been absolutely swamped over the past 24 hours as GCSE maths students came online to vent their frustration on that question about Hannah and her sweets. 

Not seen it yet? This was question number 19 on yesterday's Edexcel GCSE Maths 1MA0 Higher Tier Paper 1.

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

Hannah takes at random a 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

(a) Show that n
(b) Solve n
²-n-90=0 to find the value of n.

And this was the reaction on TSR.




This was a GCSE question?!



Took A-level maths myself, still found this question very difficult.





And, yep, someone's even started a petition complaining about it

But although it might have been tough, the Hannah's sweets conundrum was also very solvable.

Kieran S was one of the first on the site with this answer to the first part of the question.



There are six orange sweets and n sweets overall. If she takes one, there is a 6/n chance of getting and orange sweet. When she takes one, there is one less orange sweet and one less sweet overall. 

If she took another orange sweet, the probability would be (6-1)/(n-1)=5/n-1. Now, you have to find the probability if she gets two orange sweets so you simply times the two fractions: 6/n * 5/n-1 = 30/n^2-n.

It tells us the probability of two orange sweets is 1/3 which means 1/3=30/n^2-n.

We need to make the denominators the same so simply times 1/3 by 30/30 which would equal 30/90. if 30/90 = 30/n^2-n, then n^2-n=90. if n^2-n=90 then n^2-n-90 will equal zero.

Still no clearer? TSR member R Williams shared these workings of the first section... 


hannah sweets

But for sheer clarity it's hard to beat the explanation shared by Shannonriley23 of the whole question.

answer a
answer b

So there you have it - Hannah had 10 sweets. Next time just have a Twix, OK Hannah?

What did you think of the question? Was it too hard for a GCSE paper?