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PS - Probability - 4 - color socks

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by karthikpandian19 » Tue Jul 24, 2012 5:14 am
A drawer contains two red socks, two white socks, and two black socks. Three socks are drawn at random from the drawer without replacement. What is the probability that two of the three socks remaining in the drawer are the same color?


(A) 3/8

(B) 2/5

(C) 3/5

(D) 5/8

(E) 2/3
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by brainturner » Tue Jul 24, 2012 7:11 am
Probability of two of the three socks remaining in the drawer are the same color
= 1 - (probability of picking three different color socks)
= 1 - (2C1*2C1*2C1/6C3)
= 1- 2/5
= [spoiler]3/5 Answer C[/spoiler]
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by Brent@GMATPrepNow » Tue Jul 24, 2012 8:00 am
karthikpandian19 wrote:A drawer contains two red socks, two white socks, and two black socks. Three socks are drawn at random from the drawer without replacement. What is the probability that two of the three socks remaining in the drawer are the same color?


(A) 3/8

(B) 2/5

(C) 3/5

(D) 5/8

(E) 2/3
We can also solve the question using probability rules.

P(two of the three remaining socks are the same color) = 1 - P(picking three different colored socks)

P(picking three different colored socks) = P(1st sock any color AND 2nd sock different color AND 3rd sock different color)
= P(1st sock any color) X P(2nd sock different color) X P(3rd sock different color)
= 1 X (4/5) X (2/4)
= 2/5

So, P(two of the three remaining socks are the same color) = 1 - (2/5)
[spoiler]= 3/5
= C[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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