An Urn Contains 1 green ball, 1 red ball, 1 yellow ball, and 1 white ball. I draw 4 balls with replacement. What is the probability that at least one color is repeated exactly twice?Solution:

Let G be the event that we get exactly two balls are green, and R for red, Y for yellow, and W for white.

We knowP{G}=P{Y}=P{R}=P{W}= $\displaystyle \frac{1}{4}\cdot\frac{1}{4}\cdot\frac{3}{4}$

So would theP{ one color being repeated exactly twice}=$\displaystyle \frac{3}{64}+\frac{3}{64}+\frac{3}{64}+\frac{3}{64 }=\frac{12}{64}$

Note: I know this is wrong, but I just need some help to push forward on this problem.

I know the sample space, $\displaystyle \Omega=4^4$

I know the probability of a sample point is, $\displaystyle \omega=\frac{1}{256}$

Does order not matter here? I am assuming it does not from how the question was asked at the end. They just want to know if it was repeated. So (G,G,Y,W) and (G,Y,W,G) are the same thing?