After a recent Edexcel GCSE paper students took to twitter to vent their frustration at the question which arose in their exam. This question stated that “There are n sweets in a bag, 6 of these are orange the rest are yellow. Hannah takes a random sweet and eats it. Following this she takes another sweet and eats it. The probability that Hannah eats two orange sweets is 1/3, show that n^2 – n – 90 = 0?”
From the comments on social media it appears that many students were stumped by what this question was asking for with many saying that “things changed tune very fast”. This question is really asking people to think about the the idea behind conditional probability. If we have n sweets in a bag and we pick an orange first then there was a 6/n chance of doing so. Following this she doesn’t replace the sweet hence there are now n-1 sweets of which 5 are now orange. Therefore because we want to pick an orange AND then another orange we know that the total probability must be,
(6/n)*(5/n-1) = 1/3 as stated in the question. Following this requires a bit of algebraic rearrangement,
30/(n(n-1)) = 1/3 => 30/(n^2-n) = 1/3 then cross multiply,
n^2 – n = 90 therefore,
n^2 – n – 90 = 0.
Having this we can go on to solving the quadratic equations to find out how many sweets were in the bag in total and were yellow.
One thing is for sure judging by the reaction from the GCSE students Hannah and her bag of sweets caused more than a little trouble this exam season. Best of luck to all those taking there exams over the coming weeks!