n sweets, 6 are orange, the rest are yellow. Sophie takes at random a sweet. She eats the sweet. Sophie then takes at random another sweet. She eats the sweet. The probability that Sophie eats two orange sweets is 1/3. Show that n² – n – 90 = 0

If Sophie 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. If Sophie 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. Which is 6/n x 5/n–1 The question tells us that the chance of Sophie getting two orange sweets is 1/3. So: 6/n x 5/n–1 = 1/3 All we need to do now is rearrange this equation.