Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Apr 2015, 10:02

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

4 dices are thrown at the same time. What is the probability

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2026
Concentration: Finance
GMAT 1: 710 Q48 V39
Followers: 24

Kudos [?]: 291 [0], given: 354

GMAT ToolKit User
Re: Really tough [#permalink] New post 20 Feb 2014, 11:21
Bunuel wrote:
roshanaslam wrote:
4 dices are thrown at the same time. What is the probability of getting ONLY 2 dices showing the same face?

A. 4/9
B. 5/9
C. 11/18
D. 7/9
E. none of the above


I suppose "only 2 dice showing the same face" means EXACTLY two? If so then:

Total # of outcomes = 6^4

Favorable outcomes = 4C2=6, choosing two dice which will provide the same face, these two dice can take 6 values, other two 5 and 4. So, favorable outcomes=4C2*6*5*4.

\(P=\frac{4C2*6*5*4}{6^4}=\frac{5}{9}\).

Answer: B.


If we have 4C2 aren't we assuming that the other two also have to be the same number? Or does it work for 2 the same number, the other two different?

I thought that we had to use 4!/2!1!1! because the last two terms were different.

Could anybody please clarify
Thanks
Cheers
J
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40493 [0], given: 5540

Re: Really tough [#permalink] New post 20 Feb 2014, 23:39
Expert's post
jlgdr wrote:
Bunuel wrote:
roshanaslam wrote:
4 dices are thrown at the same time. What is the probability of getting ONLY 2 dices showing the same face?

A. 4/9
B. 5/9
C. 11/18
D. 7/9
E. none of the above


I suppose "only 2 dice showing the same face" means EXACTLY two? If so then:

Total # of outcomes = 6^4

Favorable outcomes = 4C2=6, choosing two dice which will provide the same face, these two dice can take 6 values, other two 5 and 4. So, favorable outcomes=4C2*6*5*4.

\(P=\frac{4C2*6*5*4}{6^4}=\frac{5}{9}\).

Answer: B.


If we have 4C2 aren't we assuming that the other two also have to be the same number? Or does it work for 2 the same number, the other two different?

I thought that we had to use 4!/2!1!1! because the last two terms were different.

Could anybody please clarify
Thanks
Cheers
J


We have 4 dice (A, B, C, D).

\(C^2_4\) is the ways to select which two dice out of 4, will provide the same face: (A, B), (A, C), (A, D), (B, C), (B, D), or (C, D) . Next, these two dice can take 6 values, the remaining two 5 and 4, respectively. So, the # of favorable outcomes is \(C^2_4*6*5*4\).

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 01 Sep 2014
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 21

GMAT ToolKit User CAT Tests
Re: 4 dices are thrown at the same time. What is the probability [#permalink] New post 06 Oct 2014, 04:11
Although I did get the answer right,I could not figure out the breakup of other possibilities.And it has been bugging me.
Total possible outcomes = 6 * 6 * 6 * 6
= 1296

Possibility of having no.s on all dices same = 6 * 1
= 6

Possibility of having 3 same no.s = 6 * 5 * 4!/3!
= 120

Possibility of having 2 same no.s and 2 different= 6 * 5C2 * 4!/2!
= 6 * 10 * 12
= 720

Possibility of having 2 pairs of same no.s = 6 * 5
=30

Possibility of having all different no.s = 6 * 5 * 4* 3
= 360
Now these possibilities don't add up
6 + 120 + 720 + 30 + 360
= 1236(total is 1296 i.e. 60 more than this)
Can anybody please tell which possibilities have i missed???
Thanks
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40493 [1] , given: 5540

Re: 4 dices are thrown at the same time. What is the probability [#permalink] New post 06 Oct 2014, 07:08
1
This post received
KUDOS
Expert's post
arpitsharms wrote:
Although I did get the answer right,I could not figure out the breakup of other possibilities.And it has been bugging me.
Total possible outcomes = 6 * 6 * 6 * 6
= 1296

Possibility of having no.s on all dices same = 6 * 1
= 6

Possibility of having 3 same no.s = 6 * 5 * 4!/3!
= 120

Possibility of having 2 same no.s and 2 different= 6 * 5C2 * 4!/2!
= 6 * 10 * 12
= 720

Possibility of having 2 pairs of same no.s = 6 * 5
=30


Possibility of having all different no.s = 6 * 5 * 4* 3
= 360
Now these possibilities don't add up
6 + 120 + 720 + 30 + 360
= 1236(total is 1296 i.e. 60 more than this)
Can anybody please tell which possibilities have i missed???
Thanks


This should be 90: 3*(6*5). The number of ways to split 4 dice into 2 pairs is 3:
AB - CD
AC - BD
AD - BC
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 01 Sep 2014
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 21

GMAT ToolKit User CAT Tests
Re: 4 dices are thrown at the same time. What is the probability [#permalink] New post 06 Oct 2014, 09:54
Thanks a lot for the help.
Re: 4 dices are thrown at the same time. What is the probability   [#permalink] 06 Oct 2014, 09:54

Go to page   Previous    1   2   [ 25 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Three dice are thrown. What is the probability that the firs sandra123 19 10 Sep 2013, 01:30
2 Experts publish their posts in the topic If two six-sided dice are thrown, what is the probability Skientist 4 22 Nov 2012, 14:12
5 Experts publish their posts in the topic Gambling with 4 dice, what is the probability of getting an cyberjadugar 5 24 May 2012, 00:31
A fair coin is thrown 5 times. What is the probability of davvy75 5 03 Oct 2006, 08:41
In tossing 4 fair dice, what is the probability of tossing, cloaked_vessel 10 27 Oct 2005, 17:56
Display posts from previous: Sort by

4 dices are thrown at the same time. What is the probability

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.