Marble probability (need confirmation of answer)

Gr8fu13

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A box has 3 white, 2 green, 2 red, and 1 blue marble. If two marbles are drawn one at a time without replacement, find the probability that one marble is green and one marble is red.
e. 1/4
f. 3/28
g. 1/7
h. 1/2

I first thought since the amount of green and red marbles accounted for half the marbles in the box the answer would be 1/2 chance. However, when t said that one is drawn at a time without replacement. I figured the first chance would be 1/2 but the second chance would be 2/7 because one is gone (making the total 7) and the 2 would account for the quanitity of the other color marbles in the box that I need to get. I multiplied the two and came up with 1/7 as my answer. Would this be correct? Thanks!
 
A box has 3 white, 2 green, 2 red, and 1 blue marble. If two marbles are drawn one at a time without replacement, find the probability that one marble is green and one marble is red.
e. 1/4
f. 3/28
g. 1/7
h. 1/2

I first thought since the amount of green and red marbles accounted for half the marbles in the box the answer would be 1/2 chance. However, when t said that one is drawn at a time without replacement. I figured the first chance would be 1/2 but the second chance would be 2/7 because one is gone (making the total 7) and the 2 would account for the quanitity of the other color marbles in the box that I need to get. I multiplied the two and came up with 1/7 as my answer. Would this be correct? Thanks!

That is correct.

You could also think of the events as

[first drawing red then drawing green] + [first drawing green then drawing red ]
 
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