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gmatpup: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Sat Oct 15, 2011 6:38 pm; Thanked: 1 times; Followed by:1 members

Probability - help

by gmatpup » Tue Jan 24, 2012 8:46 am

In a survey of 248 people, 156 are married, 70 self-employed, and 25% of those married are self-employed. If a person is to be randomly selected from those surveyed, what is the probability the person selected will be self-employed but not married?

A. 1/8
B. 4/31
C. 117/248
D. 1/4
E. 31/117

Answer is A

Thank you again

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Source: Beat The GMAT — Problem Solving | Tue Jan 24, 2012 8:46 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 24, 2012 9:27 am

gmatpup wrote:In a survey of 248 people, 156 are married, 70 self-employed, and 25% of those married are self-employed. If a person is to be randomly selected from those surveyed, what is the probability the person selected will be self-employed but not married?

A. 1/8
B. 4/31
C. 117/248
D. 1/4
E. 31/117

Answer is A

Thank you again

There are 156 married people, and "25% of those married are self-employed"
25% of 156 = 39
So, of the 156 married people, 39 are self-employed.

Now since there are 70 self-employed people in total, and since 39 of them are married, we know that 31 people are self-employed and not married (70-39=31).

So, out of 248 people, there are 31 people who are self-employed and not married.

So the probability that the selected person is self-employed but not married = 31/248 = 1/8 = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com