# Probability Question for GMAT Exam. Getting the seat you want in a crowded room.

• May 16th 2012, 02:29 AM
Cuchulainn
Probability Question for GMAT Exam. Getting the seat you want in a crowded room.
Hi - i have just joined this forum, so I hope i'm using it correctly. I'm currently preparing to do the GMAT exam and have just done a problem on one of the kaplan quizzes, which made me think of my own slightly different version, and was hoping someone could confirm my approach to my own version is correct or not!

A square table seats 1 person on each of the four sides, with every person directly facing another person across the table. If there are eight people looking to sit at this table and choose their seats at random, what is the probability that any two of the 8 getting seats directly facing each other?

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My approach:

Choose two people A and B.
Probability of A getting a seat at table is 1/2.
Probability of B getting a seat at the table once A has taken one is 3/7.
Probability of B getting a seat once A has taken one and sits opposite A is (1/3)(3/7) = 1/7.

So Answer = (1/2)(1/7) = 1/14

Is this approach correct?
• May 16th 2012, 07:02 AM
Plato
Re: Probability Question for GMAT Exam. Getting the seat you want in a crowded room.
Quote:

Originally Posted by Cuchulainn
A square table seats 1 person on each of the four sides, with every person directly facing another person across the table. If there are eight people looking to sit at this table and choose their seats at random, what is the probability that any two of the 8 getting seats directly facing each other?

So Answer = (1/2)(1/7) = 1/14

Although i did it an entirely different way, I got that same answer.
• May 17th 2012, 06:02 AM
Cuchulainn
Re: Probability Question for GMAT Exam. Getting the seat you want in a crowded room.
Thank you Plato, you've made it clearer for me. I think we're both right....I've just gone about it a slightly more long-winded way!! Thanks again!