Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Diana is going on a school trip along with her two brothers, [#permalink]
09 Jul 2010, 16:16

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

51% (02:27) correct
49% (01:54) wrong based on 100 sessions

Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?

A. 1/27 B. 4/27 C. 5/27 D. 4/9 E. 5/9

Friends, the explanation is given in the princeton review book, but i am not able to follow their explanation.

Re: Probability Qs from Princeton Review [#permalink]
09 Jul 2010, 16:56

6

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

rpgmat2010 wrote:

Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?

Friends, the explanation is given in the princeton review book, but i am not able to follow their explanation.

Please comment and explain

Diana and her two brothers can be assigned to one of the 3 groups, so each has 3 choices, so total # of different assignments of Diana and her 2 brothers to 3 groups is \(3*3*3=3^3=27\).

Now, "Diana leaves at the same time as AT LEAST one her brothers" means that Diana is in the same group as at least one her brothers.

Let's find the opposite probability of such event and subtract it from 1. Opposite probability would be the probability that Diana is not in the group with any of her brothers.

In how many ways we can assign Diana and her two brothers to 3 groups so that Diana is not in the group with any of her brothers? If Diana is in the first group, then each of her two brothers will have 2 choices (either the second group or the third) and thus can be assigned in \(2*2=2^2=4\) ways to other two groups. As there are 3 groups, then total # of ways to assign Diana and her 2 brothers to these groups so that Diana is not in the group with any her bothers is \(3*4=12\) (For each of Diana's choices her brother can be assigned in 4 ways, as Diana has 3 choices: first, second or the third group, then total \(3*4=12\)). So probability of this event is \(\frac{12}{27}\).

Probability that Diana is in the same group as at least one her brothers would be \(1-\frac{12}{27}=\frac{15}{27}=\frac{5}{9}\).

Re: Probability Qs from Princeton Review [#permalink]
09 Apr 2011, 02:49

bunuel, need your help. u r marvellous in ur approach. i went through all of them.i think my problem areas are permutation/probability. i understand though ur approaches. could you explain me, the basic way to approach such problems?the way to understand the independent, mutually exclusive, both combined, permutation/combination approach?meaning hw cn a problem be broken down to understand which approach to apply? _________________

"When the going gets tough, the tough gets going!"

Re: Probability Qs from Princeton Review [#permalink]
09 Apr 2011, 23:14

2

This post received KUDOS

1

This post was BOOKMARKED

For "atleast" problems, its easier to do (1 - opposite of what is being asked). Here 1 - different groups

# of ways in which Diana can be assigned a group = 3 # of ways in which Bruce can be assigned a group = 2 (since bruce cannot be assigned the same group as diana) # of ways in which Clerk can be assigned a group = 2 (since clerk cannot be assigned the same group as diana)

Re: Probability Qs from Princeton Review [#permalink]
25 Aug 2011, 04:37

Bunuel wrote:

rpgmat2010 wrote:

Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?

Friends, the explanation is given in the princeton review book, but i am not able to follow their explanation.

Please comment and explain

Diana and her two brothers can be assigned to one of the 3 groups, so each has 3 choices, so total # of different assignments of Diana and her 2 brothers to 3 groups is \(3*3*3=3^3=27\).

Now, "Diana leaves at the same time as AT LEAST one her brothers" means that Diana is in the same group as at least one her brothers.

Let's find the opposite probability of such event and subtract it from 1. Opposite probability would be the probability that Diana is not in the group with any of her brothers.

In how many ways we can assign Diana and her two brothers to 3 groups so that Diana is not in the group with any of her brothers? If Diana is in the first group, then each of her two brothers will have 2 choices (either the second group or the third) and thus can be assigned in \(2*2=2^2=4\) ways to other two groups. As there are 3 groups, then total # of ways to assign Diana and her 2 brothers to these groups so that Diana is not in the group with any her bothers is \(3*4=12\) (For each of Diana's choices her brother can be assigned in 4 ways, as Diana has 3 choices: first, second or the third group, then total \(3*4=12\)). So probability of this event is \(\frac{12}{27}\).

Probability that Diana is in the same group as at least one her brothers would be \(1-\frac{12}{27}=\frac{15}{27}=\frac{5}{9}\).

Answer: E.

Hope it's clear.

Bunuel! I got the same answer but I cannot really identify if my approach was a different way to get the same result or just a matter of luck.

I also substract the opposite probability: 1- P(ALL DIFERENT GROUPS)= 1-3C1x3/3x2/3x1/3x3!=5/9

My line of thought: 3C1: which group will be chose first 3/3: Any of the 3 groups cann be selected 2/3: prob of selecting any of the remainder 2 1/3: prob of selecting the remainder group 3! Number of ways the first selection can be made

Where I am wrong?

Thanks not just for your reply but for your amazing willingness to help.

Re: Diana is going on a school trip along with her two brothers, [#permalink]
04 Aug 2013, 06:44

why we did 3x3x3 for assignment or distribution ?

why we have not considered cases of 0,1,2,3 ways of distribution of three people in three groups.

n+r-1Cr-1 looks much appropriate to find all possible cases.

5!/2! = 60 ways to distribute them in three groups.

G1 G2 G3 D D D B B B C C C

3X3X3 covers cases like DDD or DBD or BBB which is not a possible distribution.

Either I am not able to understand this question properly or answer choices are not correct. _________________

Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use?| 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: Diana is going on a school trip along with her two brothers, [#permalink]
12 Nov 2014, 07:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Diana is going on a school trip along with her two brothers, [#permalink]
26 Jun 2015, 03:20

Bunuel wrote:

rpgmat2010 wrote:

Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?

Friends, the explanation is given in the princeton review book, but i am not able to follow their explanation.

Please comment and explain

Diana and her two brothers can be assigned to one of the 3 groups, so each has 3 choices, so total # of different assignments of Diana and her 2 brothers to 3 groups is \(3*3*3=3^3=27\).

Now, "Diana leaves at the same time as AT LEAST one her brothers" means that Diana is in the same group as at least one her brothers.

Let's find the opposite probability of such event and subtract it from 1. Opposite probability would be the probability that Diana is not in the group with any of her brothers.

In how many ways we can assign Diana and her two brothers to 3 groups so that Diana is not in the group with any of her brothers? If Diana is in the first group, then each of her two brothers will have 2 choices (either the second group or the third) and thus can be assigned in \(2*2=2^2=4\) ways to other two groups. As there are 3 groups, then total # of ways to assign Diana and her 2 brothers to these groups so that Diana is not in the group with any her bothers is \(3*4=12\) (For each of Diana's choices her brother can be assigned in 4 ways, as Diana has 3 choices: first, second or the third group, then total \(3*4=12\)). So probability of this event is \(\frac{12}{27}\).

Probability that Diana is in the same group as at least one her brothers would be \(1-\frac{12}{27}=\frac{15}{27}=\frac{5}{9}\).

Answer: E.

Hope it's clear.

Hi Bunnel, I'm little struggle to understand why it is 2^2=4[/m] ways, What does the first (2) and the (2) represent? Also why does 3*4 represent?

Thanks

gmatclubot

Re: Diana is going on a school trip along with her two brothers,
[#permalink]
26 Jun 2015, 03:20

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

McCombs Acceptance Rate Analysis McCombs School of Business is a top MBA program and part of University of Texas Austin. The full-time program is small; the class of 2017...