From The Daily Mail:
There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow.
Hannah takes a 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 n^2-n-90=0
The answer, as so often, is in the question.
Rearrange "n^2-n-90=0" to "n2 - n = 90" and solve, n is obviously 10, then retrace your steps.
Probability of two oranges is: (6/n)x(5/n-1) = 30/n^2-n
We know that: "n^2-n" must be 90 (30 is one-third of 90)
As a check, substitute 10 for n in the first equation, (6/10)x(5/9) = 30/90 = one-third.
Is there anything more to it than that?
Debate Magazine
