There are n sweets in a bag. 6 of them are orange, the rest are yellow. Hannah takes a random sweet, she eats the sweet and repeats again. The probability that hannah eats two orange sweets is 1/3. Show that n2 - n - 90 = 0.

The best way to think approach question is thinking of it like a tree diagram.We know there are n sweets in total. Therefore the probability of eating 1 orange sweet the first time is 6/n.The probability of hannah eating a second orange sweet (baring in mind she's already eaten one) is 5/n-1The probability of Hannah having two sweets is (6/n) x (5/n-1) = 1/3Now we want to simply to get it in the given form30/n2-n = 1/3 (multiply the brackets)n2-n = 90 (multiply by the denominators)n2-n - 90 = 0