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 YELLOW marbles are in the bag?

Answer 1

B) 5

Explanation:

The probability of picking yellow first is

x

12

. The probability of picking yellow second is

x-1

11

. This will give a solution of

x (x-1)

132

.

5

33

is equivalent to

20

132

. 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5 yellow marbles in the bag.

Answer 2

7 green, 5 yellow. Just worked backwards. C(12,2) = 66, so probability given is also 10/66

If there are x yellow marbles, then C(x,2)•C(12-x,0)/C(12,2) = 10/66. Thus C(x, 2) = 10, so x = 5 = yellows. So greens = 12–5 = 7