Question 1060190
Given that the first sock was red, there are 5 red, 7 green, and 4 blue socks left.
The probability the second sock is red is 5/16.
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probability both are red is 6/17*(5/16)=30/272
probability both are green is (7/17)(6/16)=42/272
probability both are blue is (4/17)*3/16)=12/272
That sum  is 84/272, or 21/68.
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the possibilities are blue/blue, blue/green, green/blue, green/green, red/blue, red/green.  All denominators are 272
B-B:12
B-G:28
G-B:28
G-G:42
R-B:24
R-G:42
182
182/272.
Of those 182, 40 are blue. The probability is 40/182=0.220
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a rough way to check it is that the probability the first sock is blue is 4/17 or 0.235.  If we look at what the second sock can't be red, then being blue is one possibility.  If that is the case, it lessens the likelihood of the first sock's also being blue.