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# A drawer contains 8 socks, and 2 socks are selected at

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Director
Joined: 01 Apr 2008
Posts: 783
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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12 Nov 2009, 08:35
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00:00

Difficulty:

85% (hard)

Question Stats:

44% (01:11) correct 56% (00:59) wrong based on 767 sessions

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A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.
(2) The probability is more than 0.8 that the first sock is white.
Math Expert
Joined: 02 Sep 2009
Posts: 50619

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12 Nov 2009, 08:54
14
11
Economist wrote:
A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.

(2) The probability is more than 0.8 that the first sock is white.

I suppose 8 socks means, that there are 8 and not 8 pairs.

Note that we don't know if there is any # of black socks is the drawer.
Let B be the # of black socks. And W the # of white socks.

(1) $$\frac{B}{8}<0.2$$ --> $$B<1.6$$, so there can be 1 or 0 black socks in the drawer. In any case as the # is less then 2 the probability of picking 2 black socks is 0. Sufficient.

(2) $$\frac{W}{8}>0.8$$ --> $$W>6.4$$, so there are 7 or 8 white socks in the drawer. As the maximum possible # of black socks is 1, thus the probability of 2 blacks is 0. Sufficient.

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Joined: 20 Jul 2010
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14 Sep 2010, 15:03
I had initially thought answer as D but later changed to A(my mistake). My thought process was that with second choice I don't know if remaining sock is black or not. I failed to calculate that the answer of two draws would be zero in this case also
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Joined: 16 Oct 2010
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Re: Black and White Socks  [#permalink]

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27 Nov 2010, 20:49
udaymathapati wrote:
A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?
(1) The probability is less than 0.2 that the first sock is black.
(2) The probability is more than 0.8 that the first sock is white.

How about I tell you on what lines to think and perhaps you can arrive at the answer?
Let's say there are x black socks in the drawer. When I pick the first one, the probability of picking a black sock is x/8 which is less than 1/5. Any ideas?
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Re: A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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07 Jun 2013, 05:12
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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27 Jul 2014, 05:19
Hi Bunuel, Why is that in this problem the socks are assumed to be either white or black? No where in the question is it mentioned that the socks are either white or black.

So, shouldn't the answer be E?
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Joined: 02 Sep 2009
Posts: 50619
Re: A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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27 Jul 2014, 14:51
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dilipnair27 wrote:
Hi Bunuel, Why is that in this problem the socks are assumed to be either white or black? No where in the question is it mentioned that the socks are either white or black.

So, shouldn't the answer be E?

We are not assuming that.

From (1) we have that there could be 1 or 0 black socks in the drawer (for example, there could be 1 black and 7 red socks, or all red socks). No, matter which it is, the probability of picking 2 black socks is 0.

From (2) we have that there could be 7 or 8 white socks in the drawer (for example, there could be 7 white and 1 green, or 7 white and 1 black, or 8 white socks). So, there could be at most 1 black sock (0 or 1). So, in any case the probability of picking 2 black socks is 0.

The bottom line is that, from each statement we have that the maximum number of black socks is 1, which makes the probability of picking 2 black socks equal 0.

Does this make sense?
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GMAT 2: 750 Q49 V42
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Re: A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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13 Sep 2016, 04:11
Economist wrote:
A drawer contains 8 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is less than 0.2 that the first sock is black.
(2) The probability is more than 0.8 that the first sock is white.

Number of Socks HAS to be an integer. Therefore, (1) & (2) are saying the same thing because

$$\frac{(Favorable Cases)}{(Total Number of Cases)} = Probability$$

=> Favorable Cases = Probability * Total Number of Cases

=> Number of Ways to pick a Black Sock in 1st Attempt = Prob. * 8

(1) The probability is less than 0.2 that the first sock is black. => Prob of 1at Black sock < 0.2

(2) The probability is more than 0.8 that the first sock is white. => Prob of 1st white > 0.8
=> Prob of 1st sock of any color other than white < 0.2

Therefore, Prob of 1st Black Sock < 0.2

Hence, the answer cannot be anything but D or E. D if the statement is sufficient otherwise E.

Now, Number of Ways to pick a Black Sock in 1st Attempt < 0.2 * 8 < 1.6
Hence, we have 0 or 1 Black sock.

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Re: A drawer contains 8 socks, and 2 socks are selected at  [#permalink]

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15 Nov 2018, 10:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A drawer contains 8 socks, and 2 socks are selected at &nbs [#permalink] 15 Nov 2018, 10:33
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