PIC: This Is The Maths Question (And Solution) That Drove The Internet Crazy This Week

If you were reminiscing over surviving the Leaving Cert this week, chances are this question could bring you back to the horror of Honours Maths. Twitter was flooded with students panicking over this tricky maths question that appeared on 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.’ A game of probability, the question proved difficult for the vast majority of teens sitting down to the paper. We’re not going to lie, we may have tried to master this one ourselves, but were a little stumped by the logic. So now The Guardian have worked out how to solve Hannah’s sugar conundrum: 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. (Bear with us...) 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. 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 Now, students had to rearrange the equation to prove the original equation: (6x5)/n(n-1) = 30/(n² – n) = 1/3 Or 90/(n² – n) = 1 So (n² – n) = 90 ANS: n² – n – 90 = 0 See? Simple...