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Probability

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prashant misra Really wants to Beat The GMAT! Default Avatar
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Post Sun Nov 20, 2011 7:28 am
hmm a nice and good tricky question.

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Post Fri Nov 25, 2011 9:46 pm
danjuma 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 < 0.2 that the first sock is black.

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

Can one use the probability formula for this type of question?

Thank you
Got a PM to reply on this thread.

Total no. of socks in the drawer = 8
Since we do not how many black socks are there, so let the no. of black socks = B
Similarly, let the no. of white socks = W

(1) Probability of picking a black sock = B/8
Now it is given that B/8 < 0.2 or B < 1.6, which means that either there is 1 black socks or 0 black sock. In either case, probability of picking 2 black socks = 0; SUFFICIENT to answer the question.

(2) Probability of picking a white sock = W/8
So, W/8 > 0.8 or W > 6.4, which implies there can be either 7 or 8 white socks in the drawer. If there are 7 white socks, then there is only 1 black socks and in case there are 8 white socks, then the black sock is 0. So, in either case the required probability is again 0; SUFFICIENT to answer the question.

The correct answer is D.

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Post Fri Nov 25, 2011 10:21 pm
Thanks Anurag for the help.

This was tricky!! Nice learning.

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Post Sun Nov 27, 2011 10:26 pm
clean D both the cases black socks = 1 or less.

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mourinhogmat1 Rising GMAT Star Default Avatar
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Post Sat Feb 18, 2012 8:30 pm
No where in the question does it say that the drawer contains ONLY Black and White socks right?
So, the answer should be A, right?

With B, what if there is a blue socks and a yellow socks?

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Post Mon Feb 20, 2012 1:44 pm
mourinhogmat1 wrote:
No where in the question does it say that the drawer contains ONLY Black and White socks right?
So, the answer should be A, right?

With B, what if there is a blue socks and a yellow socks?
In that case also we will get P(Two black socks)=0 because if 7 are white and rest one is yellow or pink or whatever color, then from where we will draw black sock. I think you got it....

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Post Thu Mar 29, 2012 7:57 am
I will go for (D)
Nice explanation.

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Post Sat Mar 31, 2012 4:23 am
Yes the correct answer does come out to be D. I made some difficulty in calculating the statement 1 of this question...

Otherwise the whole question was ok....

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Post Sun Sep 16, 2012 11:18 pm
Difficult for me

but was able to know both options are telling the same so guess would be D

Nice explanations though

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Post Tue Sep 18, 2012 11:01 am
OA is D

why?

if x is the no of black shocks then P(x) as per questions will be x/8*x-1/8 where x >= 2

A. x/8 < 0.2 ie x < 1.6 or x = 0 or 1 , in that case P(x) = 0
B. y/ 8 < 0.8 ie y = 7 or 8 ie x = 1 or 0 , again same

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Post Thu Apr 04, 2013 2:26 am
D is the Answer.

STATEMENT I:

P(FIRST BLACK) = 1/8

P(TWO BLACKs) = 0

STATEMENT II:

P(FIRST WHITE)=7/8 which implies P(FIRST BLACK) = 1/8 or 0/8

i.e. P(TWO BLACKs) = 0

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Post Fri Dec 26, 2014 2:18 am
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.

Not good at probability Qs.

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Post Fri Dec 26, 2014 9:07 am
Hi jaspreetsra,

In this types of probability-based DS questions, it's important to be a little cynical. Ask yourself "what was I really told?", be prepared to take lots of little notes (stay organized) and be prepared to go to extremes.

Here, we're told that there are 8 socks and that 2 are selected at random without replacement. We're asked for the probability that they're BOTH BLACK. To start, we do NOT know what color the 8 socks are. Maybe they're all 1 color, maybe they're 2 colors,....maybe they're 8 different colors...

Now, imagine if there are...
NO black socks at all, then the probability is 0%
JUST 1 black sock, then the probability is still 0%
ALL black socks, then the probability is 100%

2 or more black socks will require us to do an actual calculation.

Fact 1: The probability is LESS than .2 (meaning less than 20%) that the first sock is black

Here, we have to focus on pulling that 1st sock.

0/8 = 0
1/8 = .125
2/8 = .25
3/8 = .375
Etc.

Since the probability is LESS than .2, there are only 2 possibilities:
1 black sock....so the probability of pulling 2 black socks is 0%
or
0 black socks...so the probability of pulling 2 black socks is 0%

Under these conditions, the probability is ALWAYS 0%
Fact 1 is SUFFICIENT

Fact 2: The probability is MORE than .8 that the first sock is white.

This is essentially the same information that we had in Fact 1:

6/8 = .75
7/8 = .875
8/8 = 1

This tells us that 7 OR 8 of the socks are white (meaning they are NOT black)
7 white socks --> 0 or 1 BLACK socks --> probability of pulling 2 black socks = 0%
8 white socks --> 0 BLACK socks --> probability of pulling 2 black socks = 0%

Under these conditions, the probability is ALWAYS 0%
Fact 2 is SUFFICIENT

Final Answer: D

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