A box contains 1 green, 2 yellow, and 3 red marbles. Two marbles are drawn at random without replacement. What are the odds of drawing two different colors?

Question

anonymous · Answer

this is not that easy i don't think
plus we have to remember that you are asked for "odds' not "probability"

anonymous · Answer

probably easiest to figure out the probability of getting two of the SAME color

anonymous · Answer

Ok

anonymous · Answer

could be two yellow 
that would be 
$$\frac{2}{6}\times\frac{1}{5}=\frac{1}{15}$$

anonymous · Answer

So that's yellow... But there's only 1 green, so I can't have two of those...

anonymous · Answer

of could be two red

anonymous · Answer

that would be 
$$\frac{3}{\binom{6}{2}}=\frac{3}{15}$$

anonymous · Answer

add and get 
$$\frac{4}{15}$$ as the probability of getting two of the same color
so $$\frac{11}{15}$$ of getting different colors 
but that is not the answer

anonymous · Answer

because you are asked for "odds" not 'probability'
11 out of 15 times get different colors
4 out of 15 get the same
odds are 11:4

anonymous · Answer

Oh, I get it! Thank you so much :)

anonymous · Answer

yw