Question

There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag, without replacing the first one picked. The probability that both marbles will be yellow is
5/33
How many GREEN marbles are in the bag?

Answer 1

The equation you would use to find the probability of two yellows is:
x/12 * (x-1)/11 = 5/33
Simplifying:
(x^2-x)/132 = 5/33
Cross-multiplying:
33(X^2-x) =5*132
x^2-x = (5*132)/33
x^2-x = 20
x^2-x-20 = 0
Factor to solve for x
(x-5)(x+4) = 0
x - 5 or -4, but it has to be positive because of the context so there were 5 yellow marbles to start and so there were 7 green marbles.