Question 981078: If a drawer has 4 red socks and 4 blue socks
a) if 2 are drawn what is the probability of a match?
b) if 3 are drawn what is the probability of a match?
c) What is the probability of having all one color after 4 draws?
I have this so far..
a) 3/7
P (Red) on first draw = 4/8
P (Red) on second draw = 3/7
4/8 * 3/7 = 12/56
P (Blue) is the same so
12/56 + 12/56= 3/7
b)100% chance
c) no clue what steps to take.
Any help is appreciated!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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
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