Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 18 Jun 2013, 15:38
Customize  |  Hide

Search
Register
New posts
Unanswered

If the probability of Sita getting selected to a school is

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
Senior Manager
Senior Manager
Joined: 21 Jan 2010
Posts: 274
Followers: 0

Kudos [?]: 29 [0], given: 11

GMAT Tests User
If the probability of Sita getting selected to a school is [#permalink] New post 13 Apr 2012, 16:35
00:00

Question Stats:

76% (01:50) correct 23% (02:11) wrong based on 26 sessions
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125


My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?
[Reveal] Spoiler: OA
3 KUDOS received
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 12094
Followers: 1875

Kudos [?]: 10094 [3] , given: 959

GMAT Tests User CAT Tests
Top Member of the Month
Re: If the probability of Sita getting selected to a school is [#permalink] New post 13 Apr 2012, 16:54
3
This post received
KUDOS
vdadwal wrote:
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125


My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?


It's much better to calculate the probability of the opposite event, which would be that Sita will be rejected by all three schools, and subtract that value from 1: P=1-(\frac{4}{5})^3=\frac{61}{125}.

Direct approach:
The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:

1. She is selected by only one school: P(SRR)=\frac{3!}{2!}*\frac{1}{5}*\frac{4}{5}*\frac{4}{5}=\frac{48}{125} (S stands for selected and R stands for rejected). We are multiplying by \frac{3!}{2!}, since SRR scenario can occur in several ways: SRR, RSR, RRS, (so \frac{3!}{2!} is # of permutations of 3 letters SRR out of which 2 R's are identical);

2. She is selected by only two school: P(SSR)=\frac{3!}{2!}*\frac{1}{5}*\frac{1}{5}*\frac{4}{5}=\frac{12}{125}, the same reason of multiplying by \frac{3!}{2!};

3. She is selected by all three school: P(SSS)=(\frac{1}{5})^3=\frac{1}{125}, we are not multiplying this time since SSS can occur only in one way.

So P=\frac{48}{125}+\frac{12}{125}+\frac{1}{125}=\frac{61}{125}.

Answer: C.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Manager
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 243
Schools: Johnson '15
Followers: 2

Kudos [?]: 14 [0], given: 16

GMAT Tests User
Re: If the probability of Sita getting selected to a school is [#permalink] New post 14 Apr 2012, 00:36
Bunuel wrote:
vdadwal wrote:
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125


My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?


It's much better to calculate the probability of the opposite event, which would be that Sita will be rejected by all three schools, and subtract that value from 1: P=1-(\frac{4}{5})^3=\frac{61}{125}.

Direct approach:
The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:

1. She is selected by only one school: P(SRR)=\frac{3!}{2!}*\frac{1}{5}*\frac{4}{5}*\frac{4}{5}=\frac{48}{125} (S stands for selected and R stands for rejected). We are multiplying by \frac{3!}{2!}, since SRR scenario can occur in several ways: SRR, RSR, RRS, (so \frac{3!}{2!} is # of permutations of 3 letters SRR out of which 2 R's are identical);

2. She is selected by only two school: P(SSR)=\frac{3!}{2!}*\frac{1}{5}*\frac{1}{5}*\frac{4}{5}=\frac{12}{125}, the same reason of multiplying by \frac{3!}{2!};

3. She is selected by all three school: P(SSS)=(\frac{1}{5})^3=\frac{1}{125}, we are not multiplying this time since SSS can occur only in one way.

So P=\frac{48}{125}+\frac{12}{125}+\frac{1}{125}=\frac{61}{125}.

Answer: C.

Hope it's clear.


BB's answers are 99.99999 times crystal clear.. :)

thanks for the explanation BB
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Re: If the probability of Sita getting selected to a school is   [#permalink] 14 Apr 2012, 00:36
    Similar topics Author Replies Last post
Similar
Topics:
 New posts School selection? just4fun 5 15 Jan 2005, 15:37
New posts Experts publish their posts in the topic School selection carsen 6 16 Jan 2005, 10:06
Popular new posts Probable to get probability questions ??? jinesh 10 06 Jan 2006, 05:31
New posts 1 Probability of Getting into Business School Michmax3 9 23 Sep 2010, 10:26
New posts Can somebody get selected in top b schools with this profile mnbhshn 2 01 Nov 2010, 19:53
Display posts from previous: Sort by

If the probability of Sita getting selected to a school is

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: VeritasPrepKarishma, Bunuel, IanStewart

Search for:


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com