probability doubt

Expert replies

crackinggmat: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Thu Jun 03, 2010 11:58 am; Thanked: 1 times

by crackinggmat » Wed Aug 24, 2011 5:32 pm

Sam and jessica are invited to a dance .if there are 7 women and 7 womenin total at the dance, and one woman and one man are chosen to lead the dance , what is the probability that sam and jessica will not be the pair chosen to lead the dance?

1/49 1/7 6/7 47/49 48/49

I have solved this Q ,so obviously i am not looking for answer but my doubt is why can't we use the following approach....

Since we dont want jessica and sam to lead the pair ,so we can choose the pair in 6/7 * 6/7 ways
which is 36 /49 but this is wrong .where i am wrong....

Source: Beat The GMAT — Problem Solving | Wed Aug 24, 2011 5:32 pm

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Aug 24, 2011 7:06 pm

if there are 7 women and 7 womenin total at the dance,

Hi,
I guess it is 7 men and 7 women.
Coming to the problem,
You calculation contains all pairs in which neither Sam nor Jessica is chosen. But, the question asks all pairs except the pair of Sam and Jessica. There is a difference, right?
For instance, you are leaving the cases in which Sam is chosen and any of the other 6 girls except Jessica is chosen and the cases in which Jessica is chosen and any of the other 6 boys except Sam is chosen.
This adds (1/7)*(6/7) + (6/7)*(1/7) to the already calculated 36/49.
So, answer is 36/49+6/49+6/49 = 48/49.

A simpler way would be removing the case of choosing Sam and Jessica.
Sam and Jessica can be chosen as a pair with probability (1/7)*(1/7) = 1/49.
So, probability that sam and jessica will not be the pair chosen = 1-1/49 = 48/49.

Cheers!

Things are not what they appear to be... nor are they otherwise

navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Thu Aug 25, 2011 2:17 am

Thanks Frankenstein

This time no looking back!!!
Navami

czarczar: Master | Next Rank: 500 Posts; Posts: 106; Joined: Fri Feb 05, 2010 9:39 amFollowed by: 1 member; Thanked: 4 times

by czarczar » Fri Aug 26, 2011 5:57 am

Thanks Frankenstein !!!!

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review