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# A drawer contains 6 brown socks and 4 black socks.

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A drawer contains 6 brown socks and 4 black socks. [#permalink]  15 Aug 2017, 01:31
Expert's post
00:00

Question Stats:

100% (01:15) correct 0% (00:00) wrong based on 8 sessions

A drawer contains 6 brown socks and 4 black socks. What is the probability that the first two socks pulled from the drawer will be of the same color?

A. $$\frac{1}{3}$$

B. $$\frac{7}{15}$$

C. $$\frac{1}{2}$$

D. $$\frac{8}{15}$$

E. $$\frac{2}{3}$$
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1228
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Kudos [?]: 1105 [1] , given: 7

Re: A drawer contains 6 brown socks and 4 black socks. [#permalink]  15 Aug 2017, 11:32
1
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Expert's post
Carcass wrote:
A drawer contains 6 brown socks and 4 black socks. What is the probability that the first two socks pulled from the drawer will be of the same color?

A. $$\frac{1}{3}$$

B. $$\frac{7}{15}$$

C. $$\frac{1}{2}$$

D. $$\frac{8}{15}$$

E. $$\frac{2}{3}$$

P(both socks the same color) = P(the two socks are both brown OR the two socks are both black)

= P(1st is brown AND 2nd is brown) + P(1st is black AND 2nd is black)

= [P(1st is brown) x P(2nd is brown)] + [P(1st is black) x P(2nd is black)]

= [6/10 x 5/9] + [4/10 x 3/9]

= 30/90 + 12/90

= 42/90

= 7/15

[Reveal] Spoiler:
B

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Re: A drawer contains 6 brown socks and 4 black socks.   [#permalink] 15 Aug 2017, 11:32
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