gmatprep probability

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vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

by vkb16 » Mon May 04, 2009 6:55 am

A and B work at a factory with 4 other workers. For a survey, 2 out of the 6 employees will be selected. Whats the prob. that both A and B will be selected?

1/15

1/12

1/9

1/6

1/3

OA is A

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Source: Beat The GMAT — Data Sufficiency | Mon May 04, 2009 6:55 am

mike22629: Master | Next Rank: 500 Posts; Posts: 322; Joined: Fri Mar 27, 2009 3:56 pm; Thanked: 24 times; GMAT Score:710

by mike22629 » Mon May 04, 2009 9:36 am

With probability problems on GMAT, I have found that it is often best to first find the total number of possibilities.

There are 6 Total workers and it is asking for comibinations of 2.

To find Total: 6C2 = 6!/(2!*4!) This is combinations formula
= 15

Now find how many different ways A and B can be chosen. There are only two of them, and you have to choose 2, so there is only 1 possibility.
(Note that order does not matter, so the Combinations formula is used. If the question said that the order that the people were surveyed mattered, then the Permuations Formula should be used)

So there answer is 1/15

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artistocrat: Master | Next Rank: 500 Posts; Posts: 152; Joined: Wed Mar 12, 2008 4:36 pmFollowed by: 2 members; Thanked: 8 times

easy solution

by artistocrat » Mon May 04, 2009 11:42 am

chances are 2/6 that A or B will be chosen on the first pick. chances are then 1/5 that the remaining A or B will be chosen. So,

2/6*1/5=2/30=1/15

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