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A drawer contains 8 socks, and 2 socks are selected at random without

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A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 12 Nov 2009, 09:35
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A
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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.
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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 12 Nov 2009, 09:54
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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.

Answer: D.
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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 14 Sep 2010, 16:03
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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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 27 Nov 2010, 21:49
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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.

Please explain in detail.


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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New post 07 Jun 2013, 06:12
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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 27 Jul 2014, 06:19
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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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 27 Jul 2014, 15:51
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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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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 13 Sep 2016, 05:11
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.

Answer: D
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Re: A drawer contains 8 socks, and 2 socks are selected at random without  [#permalink]

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New post 09 Dec 2018, 01:03
Bunuel wrote:
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.

Answer: D.


Bunuel, after calculating the range in each statements, how did you deduce the fact (highlighted in red) and concluded that black socks are 0 ( highlighted in blue)?
I still can't get what am I missing! :(
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Re: A drawer contains 8 socks, and 2 socks are selected at random without   [#permalink] 09 Dec 2018, 01:03
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