'Hannah's Sweet Question'

So, my exams finished yesterday (well all but one, but we'll ignore that S2 exists shall we?) and on the theme of exams, yesterday I saw the 'evil' 'Hannah's Sweet question' which stumped some GCSE Edexcel students earlier this week. 

During an exam, when you're working like crazy against the clock to finish the paper, it is very easy to panic when a question is unlike any you've seen before. 'Hannah's sweet question' is a combination of algebra and probability which is why, I think, it stumped some GCSE students.

My solution to 'Hannah's Sweet Problem': 

On first sight, this question looks horrible. But if you think about it, scribble a few things down then the answer becomes clear.

Drawing a tree diagram to show the probabilities of picking two oranges sweets, an orange sweet and a yellow sweet, a yellow sweet and an orange sweet or two yellow sweets helps make the question clearer. The important part of the tree diagram is circled in white.

We're told that the probability that Hannah eats two oranges sweets is 1/3. By drawing a tree diagram we can see that the probability of eating two oranges sweets is 6/n multiplied by 5/n-1.

The probability of getting an orange sweet the first time is 6/n because there are 6 orange sweets and a total of n sweets she is choosing from.

The probability of getting an orange sweet the second time is 5/n-1 because, if she has taken an orange sweet the first time then, there are only 5 orange sweets left and there is a totally of n-1 sweets left in the bag.

And there you have it, the solution to 'Hannah's Sweet Problem.

The key to doing this question is to stay calm. If your immediate reaction to a difficult question is 'oh my gosh, how am I meant to do this?!', then not only will you not be able to do the question you're stuck on but you will have problems with the rest of the paper because you're in a panic.

Any questions about the method, ask me in the comments!