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Probability question - Need expert help

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Probability question - Need expert help

by voodoo_child » Fri Jul 13, 2012 8:57 am
If a bin contains twenty cards numbered 1, 2, ..., 20, what is the probability that the sum of the numbers on two cards extracted from the bin will be even?

a) 1/2
b) 9/19
3) ....

OA - b)

How do I know whether the cards are drawn with or without replacement? There is nothing indicated in the question. The source of this question is GMATClub. I am not sure how GMAC would ask such a question. Any thoughts?

With replacement => prob = 1/2
Without replacement => prob = 9/19. The calculation is straightforward for both the options.


Thoughts?

NB - Experts: I am NOT LOOKING FOR THE SOLUTION BUT THE ANSWER TO MY QUESTION ABOVE.

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by KapTeacherEli » Fri Jul 13, 2012 10:00 am
Hi voodoo_child,

Note the language "the numbers on two cards." This unambiguously means two separate cards! If it were phrased, "two cards are drawn from the bin," or worse, "after two draws from the bin," then there might be untestlike lack of clarity. But here, there is no doubt that there is no replacement.

Hope this helps!
Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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by shekhar.kataria » Sat Jul 14, 2012 4:44 am
Hi KapTeacherEli

Even i was stumped at the same point. I now understand the difference in the phrases after your explanation. Thanks

However, the question is will GMAC use such confusing phrases in test Questions. If yes, Can you please point out any sample question, which has this much level of confusion in language, from GMAC authenticated source or from any OG book,


KapTeacherEli wrote:Hi voodoo_child,

Note the language "the numbers on two cards." This unambiguously means two separate cards! If it were phrased, "two cards are drawn from the bin," or worse, "after two draws from the bin," then there might be untestlike lack of clarity. But here, there is no doubt that there is no replacement.

Hope this helps!
Restlessness and discontent are the first necessities of progress.--Thomas A. Edison

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by KapTeacherEli » Sat Jul 14, 2012 9:06 am
shekhar.kataria wrote:Hi KapTeacherEli

Even i was stumped at the same point. I now understand the difference in the phrases after your explanation. Thanks

However, the question is will GMAC use such confusing phrases in test Questions. If yes, Can you please point out any sample question, which has this much level of confusion in language, from GMAC authenticated source or from any OG book,


KapTeacherEli wrote:Hi voodoo_child,

Note the language "the numbers on two cards." This unambiguously means two separate cards! If it were phrased, "two cards are drawn from the bin," or worse, "after two draws from the bin," then there might be untestlike lack of clarity. But here, there is no doubt that there is no replacement.

Hope this helps!
Here's a basic rule that should clear things up:

If you are told you are selecting multiple objects-- "three markers," "four fruit," "two cards," you can always assume they are selected without replacement--three makers, for instance, means "three different markers" by definition. Of course, the GMAT might include language like "without replacement" anyway, just to play safe, but it's not required.

The ambiguity that must be avoid comes from referencing the selections themselves--"the sum of two selections," "two draws from a deck," "your third fruit choice," "the result of the fourth drawing in the lottery." But you never need to worry, because the GMAT will always specify that there is no replacement (or that there is replacement!) if there is significant ambiguity in the question text.
Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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