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14 Nov 2016, 08:12
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A drawer contains 6 socks. If two socks are randomly selected without replacement, what is the probability that both socks will be black?
(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.
* Kudos for all correct solutions
(1) The probability is less than 0.3 that the first sock selected will be black.
(2) The probability is greater than 0.4 that both socks will be white.
* Kudos for all correct solutions
Here's our video solution: https://www.gmatprepnow.com/module/gmat ... /video/764
16 Nov 2016, 03:40
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S1 - Probability of selecting 1 black sock from 6 socks =\(\frac{bC1}{6C1}\)=\(\frac{b}{6}\)<0.3
where b is no. of black socks.
i.e. b<1.8 i.e. b can be 0 or 1.
In either case the probability is 0. So sufficient.
S2 - Probability of both socks white >0.4
i.e.\(\frac{wC2}{6C2}\) >0.4 where w is no. of white socks
\(\frac{w(w-1)}{30}\)> 0.4
therefore, w>4 i.e. no. of white socks is 5 or 6.
In either case, probability of picking 2 black socks is 0. So, sufficient.
Hence answer is D.
If u find my post useful, please press kudos!
where b is no. of black socks.
i.e. b<1.8 i.e. b can be 0 or 1.
In either case the probability is 0. So sufficient.
S2 - Probability of both socks white >0.4
i.e.\(\frac{wC2}{6C2}\) >0.4 where w is no. of white socks
\(\frac{w(w-1)}{30}\)> 0.4
therefore, w>4 i.e. no. of white socks is 5 or 6.
In either case, probability of picking 2 black socks is 0. So, sufficient.
Hence answer is D.
If u find my post useful, please press kudos!
14 Nov 2016, 15:10
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GMATPrepNow
The number of black socks and white socks have to be integers
let's call The number of black socks b and The number of white socks w
(1) The probability is less than 0.3 that the first sock selected will be black.
it means that \(\frac{b}{6}<0.3\) ===> \(b<1.8\)=====> \(b<=1\)
Thus, there is not possibility to selected without replacement 2 black socks because there is only one of those or none of those.
probability=0 SUFFICIENT
(2) The probability is greater than 0.4 that both socks will be white.
\(\frac{w}{6}*(w-1)/5>0.4\) w*(w-1)>12 the lowest integer for w is 5
Thus there are 1 or less black socks
again there is not possibility to selected without replacement 2 black socks
probability=0 SUFFICIENT
answer D
