BTGmoderatorDC wrote:A container contains 4 red marbles and 8 blue marbles. A second container contains 6 red marbles and x blue marbles. One marble is drawn from each of the two containers. If the probability of drawing a pair of marbles of the same color is 1/2, what is the value of x?

A. 0
B. 4
C. 6
D. 10
E. 12

We can PLUG IN THE ANSWERS, which represent the value of x.
The probability of drawling 2 of the same color = P(both marbles are red) or P(both marbles are blue) = P(RR) + P(BB).
When the correct answer is plugged in, we get:
P(RR) + P(BB) = 1/2

B: 4 --> 1st container = 4 red and 8 blue, 2nd container = 6 red and 4 blue
P(RR) + P(BB) = (4/12 * 6/10) + (8/12 * 4/10) = 3/15 + 4/15 = 7/15
Here, the resulting probability is less than 1/2 and thus is TOO SMALL.

D: 10 --> 1st container = 4 red and 8 blue, 2nd container = 6 red and 10 blue
P(RR) + P(BB) = (4/12 * 6/16 + (8/12 * 4/16) = 3/24 + 10/24 = 13/24
Here, the resulting probability is greater than 1/2 and thus is TOO BIG.

Since B yields a result that is TOO SMALL, while D yields a result that is TOO BIG, the correct answer must between B and D.

The correct answer is C.

C: 6 --> 1st container = 4 red and 8 blue, 2nd container = 6 red and 6 blue
P(RR) + P(BB) = (4/12 * 6/12) + (8/12 * 6/12) = 1/6 + 2/6 = 3/6 = 1/2
Success!