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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 8:28 am
hmm a nice and good tricky question.

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Post Fri Nov 25, 2011 10:46 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 11:21 pm
Thanks Anurag for the help.

This was tricky!! Nice learning.

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Post Sun Nov 27, 2011 11:26 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 9:30 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 2:44 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 8:57 am
I will go for (D)
Nice explanation.

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Post Sat Mar 31, 2012 5:23 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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Ganesh hatwar Rising GMAT Star Default Avatar
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Post Mon Sep 17, 2012 12:18 am
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 12:01 pm
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

rajeshsinghgmat Really wants to Beat The GMAT! Default Avatar
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Post Thu Apr 04, 2013 3:26 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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