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

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A drawer contains 8 socks, and 2 socks are selected at [#permalink] New post 12 Nov 2009, 08:35
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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: Probability socks [#permalink] New post 12 Nov 2009, 08:54
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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: Probability socks [#permalink] New post 14 Sep 2010, 02:57
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Re: Probability socks [#permalink] New post 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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Re: Black and White Socks [#permalink] New post 27 Nov 2010, 20:49
Expert's post
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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Re: A drawer contains 8 socks, and 2 socks are selected at [#permalink] New post 07 Jun 2013, 05:12
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Re: A drawer contains 8 socks, and 2 socks are selected at [#permalink] New post 25 Jun 2014, 04:06
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Re: A drawer contains 8 socks, and 2 socks are selected at [#permalink] New post 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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Re: A drawer contains 8 socks, and 2 socks are selected at [#permalink] New post 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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A drawer contains 8 socks, and 2 socks are selected at   [#permalink] 27 Jul 2014, 14:51
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