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# probability Q

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Manager
Joined: 25 Jul 2006
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16 Apr 2007, 23:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This is a repost of a Challenge question (Challenge 3, Q 26) posted several weeks back for which I have no response so far.

Store with 10 bottles of alcohol, of which 7 whiskeys.
If 6 bottles are sold, what is the prob of selling 4 whiskeys among the 6?

Given solution:
(7C4)(3C2)/(10C6) = 1/2

It seems to me that this solution assumes that 4 and only 4 whiskeys are sold. But the question doesn't exactly say that. The way the question is worded, it doesn't specify that the other 2 bottles that are sold are not whiskeys. Hence, it seems to me that we should calculate probability that atleast 4 whiskeys are sold. This gives (7C4)(6C2)/(10C6) = 5/8 as the answer (bcoz there are 6 (not 3) choices from which to pick the remaining two). Is this correct? If not, how to solve?

I am not a probability guru and would appreciate the opinion of a subject expert - since I am a little confused by this question/answer and am not sure if am on the right track.,. thanks!
Senior Manager
Joined: 01 Jan 2007
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17 Apr 2007, 02:17
oops wrote:
This is a repost of a Challenge question (Challenge 3, Q 26) posted several weeks back for which I have no response so far.

Store with 10 bottles of alcohol, of which 7 whiskeys.
If 6 bottles are sold, what is the prob of selling 4 whiskeys among the 6?

Given solution:
(7C4)(3C2)/(10C6) = 1/2

It seems to me that this solution assumes that 4 and only 4 whiskeys are sold. But the question doesn't exactly say that. The way the question is worded, it doesn't specify that the other 2 bottles that are sold are not whiskeys. Hence, it seems to me that we should calculate probability that atleast 4 whiskeys are sold. This gives (7C4)(6C2)/(10C6) = 5/8 as the answer (bcoz there are 6 (not 3) choices from which to pick the remaining two). Is this correct? If not, how to solve?

I am not a probability guru and would appreciate the opinion of a subject expert - since I am a little confused by this question/answer and am not sure if am on the right track.,. thanks!

Well your method is correct when the question stem says that there should be atlease 4 whiskey bottels among the bottels that are sold. well the question stem very specifically mentions that there should be 4 bottels of whiskeys and hence the given solution is correct. I am not a probability guru as well but I hope this will help.

Javed.

Cheers!
Director
Joined: 13 Mar 2007
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Schools: MIT Sloan
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21 Apr 2007, 16:35
well, even by going with the assumption of 'atleast' 4 bottles of whiskey.

Should'nt this be the way it needs to be solved ?

p(4W) + p(5w) + p(6w) ?

=> 7c4.3c2/10c6 + 7c5.3c1/10c6 + 7c6/10c6 ?
Manager
Joined: 28 Feb 2007
Posts: 197
Location: California
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22 Apr 2007, 12:44
oops wrote:
This is a repost of a Challenge question (Challenge 3, Q 26) posted several weeks back for which I have no response so far.

Store with 10 bottles of alcohol, of which 7 whiskeys.
If 6 bottles are sold, what is the prob of selling 4 whiskeys among the 6?

Given solution:
(7C4)(3C2)/(10C6) = 1/2

It seems to me that this solution assumes that 4 and only 4 whiskeys are sold. But the question doesn't exactly say that. The way the question is worded, it doesn't specify that the other 2 bottles that are sold are not whiskeys. Hence, it seems to me that we should calculate probability that atleast 4 whiskeys are sold. This gives (7C4)(6C2)/(10C6) = 5/8 as the answer (bcoz there are 6 (not 3) choices from which to pick the remaining two). Is this correct? If not, how to solve?

I am not a probability guru and would appreciate the opinion of a subject expert - since I am a little confused by this question/answer and am not sure if am on the right track.,. thanks!

Probability questions are very specific on at least, at most etc. Question specifies that 4 whiskey bottles were sold. since there is no at least I would go with the given explanation. My 2 cents. (Btw, I took probability in both undergrad and grad school so I can say that i have seen reasonably good number of P questions)

hth.
GMAT Club Legend
Joined: 07 Jul 2004
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22 Apr 2007, 18:55
Number of ways of picking 6 bottles from 10 = 10C6 = 210
Number of ways of picking 4 bottles of whiskey from 7 = 7C4.
Number of ways of picking 2 other bottles of alcohol = 3C2

So P = (3C2 * 7C4)/10C6
GMAT Club Legend
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22 Apr 2007, 18:57
the question says 4 whiskeys are sold. It does not assume only 4 are sold because the question clearly states that (only 4 are sold).

If it meant anything else, it would state with phrases like 'at least'.
Manager
Joined: 25 Jul 2006
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26 Apr 2007, 23:03
ywilfred wrote:
the question says 4 whiskeys are sold. It does not assume only 4 are sold because the question clearly states that (only 4 are sold).

If it meant anything else, it would state with phrases like 'at least'.

question doesn't say "only" - hence the confusion.
but you may be right in that if it means "atleast" or something else, it'll be specified.

this confusion originally came from a set theory question where if it doesn't say "18% watch exactly 2" or "only 2" in the below problem, the answer would be different - hence, i try to look for "only" or "exactly" to be clearly specified in the question.
http://www.gmatclub.com/phpbb/viewtopic ... rmontville
26 Apr 2007, 23:03
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