Question 981078
Throughout the problem, I'm assuming no replacements are made. 


a)


Case 1: You pull out a red sock on the first draw


P(drawing another red) = (# of red)/(# total)
P(drawing another red) = 3/7


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Case 2: You pull out a blue sock on the first draw


P(drawing another blue) = (# of blue)/(# total)
P(drawing another blue) = 3/7


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So either way, it's 3/7. You are correct.


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b)


You are correct. There are only two colors. By the time you get to the third draw, you'll either pick red or blue. Either you have a match in the first two draws or you will have a match with the third draw (with one of the first two draws).


So that's why it's 100% or 1.


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c)


Case 1: You draw red on the first draw


P(2nd red) = 3/7
P(3rd red) = 2/6
P(4th red) = 1/5


P(4 reds) = (3/7)*(2/6)*(1/5)
P(4 reds) = (3*2*1)/(7*6*5)
P(4 reds) = 6/210
P(4 reds) = 1/35


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Case 2: You draw blue on the first draw


P(2nd blue) = 3/7
P(3rd blue) = 2/6
P(4th blue) = 1/5


P(4 blues) = (3/7)*(2/6)*(1/5)
P(4 blues) = (3*2*1)/(7*6*5)
P(4 blues) = 6/210
P(4 blues) = 1/35



Either way, the answer is 1/35