Question

Hannah has 6 orange sweets and some yellow sweets. Overall, she has n sweets. The probability of her taking 2 orange sweets is 1/3. Prove that: n^2-n-90=0

Answer 1

The probability of her taking first orange sweet is 6/n. The probability of her taking second orange sweet is 5/(n-1). So the probability of taking 2 orange sweets is (6/n)*[5/(n-1)]=1/3. Deformation this equation, we can get that n^2-n-90=0.