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 YELLOW marbles are in the bag?

x yellow

12 - x green

first draw
x/12
second draw
(x-1)/11
so both
(x^2-x)/132 = 5/33

33(x^2-x) = 660
x^2 - x - 20 = 0
(x-5)(x+4) = 0

x = 5 because it is hard to visualize a negative yellow marble

To determine the number of yellow marbles in the bag, let's set up an equation using probability.

Let's assume that there are "x" yellow marbles in the bag and (12 - x) green marbles, as there are a total of 12 marbles in the bag.

The probability of the first marble being yellow is x/12 since there are "x" yellow marbles out of 12 marbles in the bag.

After the first yellow marble is picked, there will be (x-1) yellow marbles left and (12 - x) green marbles remaining in the bag. So, the probability of the second marble being yellow is (x-1)/(12 - 1) = (x-1)/(11).

The total probability of picking two yellow marbles without replacement can be found by multiplying the probabilities of both events occurring: (x/12) * ((x-1)/11).

According to the given information, this probability is equal to 5/33. So, we can set up the following equation:

(x/12) * ((x-1)/11) = 5/33

To solve this equation, we can cross multiply:

33 * x * (x-1) = 5 * 12 * 11

After simplifying and rearranging the equation:

33x^2 - 33x - 660 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the number of yellow marbles in the bag.