Please help-Probability

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dddanny2006: Master | Next Rank: 500 Posts; Posts: 209; Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Mon Dec 02, 2013 10:24 am

John invites 12 Friends to a dinner party,half of which are men.Exactly one man and one woman are bringing deserts.If one person from this group is selected at random ,what is the probability that it is a woman who is not bringing deserts or a man who is not bringing deserts

6 men 6 women

(5/6)dont bring deserts (5/6) dont bring deserts

Probability is (5/6)+(5/6)

I know that Im wrong.Please tell me the conceptual mistake that Im making.

Thank you

Dan

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Source: Beat The GMAT — Problem Solving | Mon Dec 02, 2013 10:24 am

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by [email protected] » Mon Dec 02, 2013 1:59 pm

Hi dddanny2006,

This question tells us that there are 12 total people (6 men and 6 women). If we're going to randomly select one person from this group, then the solution will have to be "out of 12."

We're asked for the probability of picking someone who DID NOT bring a desert (either male or female is acceptable).

We have 10 people who didn't bring a desert, so the probability is 10/12 = 5/6

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Dec 02, 2013 11:17 pm

dddanny2006 wrote:John invites 12 Friends to a dinner party,half of which are men.Exactly one man and one woman are bringing deserts.If one person from this group is selected at random ,what is the probability that it is a woman who is not bringing deserts or a man who is not bringing deserts

6 men 6 women

(5/6)dont bring deserts (5/6) dont bring deserts

Probability is (5/6)+(5/6)

I know that Im wrong.Please tell me the conceptual mistake that Im making.

Thank you

Dan

You will select one from the total, which is 12, not 6. And there are 10 such people in the group as required. Rest is well.

It's a nice idea to write down your own approach over the wrong answered questions. It helps us repair it only where it's needed. It seems that you might miss this little concept that probability of any event can never exceed 1, otherwise you should on your own be surprised to find probability (5/6) + (5/6)!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Dec 03, 2013 9:33 am

Or with more detailed processing:

M = P(MAN) = 1/2
W = P(WOMAN) = 1/2

D = P(any individual bringing a dessert) = 1/6
D' = P(...not bringing a dessert) = 5/6

P([W and D'] or [M and D']) = [1/2 * 5/6] + [1/2 * 5/6] = 5/6

I prefer Rich's method because its quicker. Thankfully my answer concurs!

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