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

It is currently 21 Aug 2014, 12:41

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

6 fair dice are tossed. What is the probability that at

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
6 fair dice are tossed. What is the probability that at [#permalink] New post 09 Oct 2007, 11:47
6 fair dice are tossed. What is the probability that at least two of them show the same face.


Pleas provide your explanations, thank you.

original post available at:

http://www.gmatclub.com/forum/t53592
Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1816
Followers: 8

Kudos [?]: 87 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 12:02
To me, we should consider the opposite case : all dices have different numbers.

P(At least 2) = 1 - P(all different)
= 1 - (6*5*4*3*2*1) / (6^6)
= 1 - 20/6^4
Senior Manager
Senior Manager
User avatar
Joined: 02 Aug 2007
Posts: 347
Location: Greater New York City area
Schools: Tuck, Ross (R1), Duke, Tepper, ISB (R2), Kenan Flagler (R2)
Followers: 3

Kudos [?]: 25 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 12:16
Atleast 2 are dice need to have same number, which means 2,3,4,5 and 6 can have same.

So we can compute the prob of all have different and subtract that from 1 which will give us the answer.

For the first dice, the prob is 1 since any value is fine.
For the second, the prob has to be other than first. So 5/6
For third, the prob has to be other than first and second. So 4/6.
For fourth, 3/6
For fifth. 2/6
For sixth, only one remains so 1/6.

So the probability is (1).(5/6).(4/6).(3/6).(2/6).(1/6) = 5/324.
So the answer is 1-5/324

Answer = 319/324
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
Re: PERMUTATION & COMBINATION gurus!!! [#permalink] New post 09 Oct 2007, 12:55
Thank you for your explanations, clear now.

one question...if it were not 6, but 5 fair dices;

5 fair dice are tossed. What is the probability that at least two of them show the same face.

to asnwer this questions can we use the same formulae:

P(At least 2) = 1 - P(all different)

i think yes, but little unsure..
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 44 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 13:10
Irina, do we know the OA of this question?
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 13:13
beckee529 wrote:
Irina, do we know the OA of this question?


I copied this question from young_gun at:

http://www.gmatclub.com/forum/p380560

he/she has not provided OA yet...
Senior Manager
Senior Manager
avatar
Joined: 27 Jul 2006
Posts: 299
Followers: 1

Kudos [?]: 6 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 19:50
five dice throws.

1-5/6*4/6*3/6*2/6*1/6
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
 [#permalink] New post 09 Oct 2007, 20:07
defenestrate wrote:
five dice throws.

1-5/6*4/6*3/6*2/6*1/6


defenestrate,

why do not we start with 6/6 and end with 2/6, instead we start with 5/6 and end with 1/6 ?

for example:

to find number of ways 6 objects can be organized in group of 6 (order matters) 6*5*4*3*2*1

to find number of ways 6 objects can be organized in group of 4 (order matters) 6*5*4*3

from here i thought we should start with 6/6 and end with 2/6...?

Please explain y not, thank you.
Manager
Manager
User avatar
Joined: 07 Sep 2007
Posts: 121
Followers: 1

Kudos [?]: 9 [0], given: 0

 [#permalink] New post 11 Oct 2007, 00:32
IrinaOK wrote:
defenestrate wrote:
five dice throws.

1-5/6*4/6*3/6*2/6*1/6


defenestrate,

why do not we start with 6/6 and end with 2/6, instead we start with 5/6 and end with 1/6 ?


Because he is wrong.


6 Dice:
1 - (6!) / 6^6 = 5!/6^5 = 120/6^5 = 1 - 120 / 7776 = 319/324

5 Dice:
1 - (6! / 1!) / 6^5 = 1 - 5!/6^4 = 1 - 120/1296 = 8/9
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
 [#permalink] New post 11 Oct 2007, 01:07
JingChan wrote:
IrinaOK wrote:
defenestrate wrote:
five dice throws.

1-5/6*4/6*3/6*2/6*1/6


defenestrate,

why do not we start with 6/6 and end with 2/6, instead we start with 5/6 and end with 1/6 ?



6 Dice:
1 - (6!) / 6^6 = 5!/6^5 = 120/6^5 = 1 - 120 / 7776 = 319/324

5 Dice:
1 - (6! / 1!) / 6^5 = 1 - 5!/6^4 = 1 - 120/1296 = 8/9


Thank you :)
Manager
Manager
avatar
Joined: 29 Jul 2007
Posts: 183
Followers: 1

Kudos [?]: 10 [0], given: 0

GMAT Tests User
 [#permalink] New post 11 Oct 2007, 02:03
IrinaOK wrote:
defenestrate wrote:
five dice throws.

1-5/6*4/6*3/6*2/6*1/6


defenestrate,

why do not we start with 6/6 and end with 2/6, instead we start with 5/6 and end with 1/6 ?

for example:

to find number of ways 6 objects can be organized in group of 6 (order matters) 6*5*4*3*2*1

to find number of ways 6 objects can be organized in group of 4 (order matters) 6*5*4*3

from here i thought we should start with 6/6 and end with 2/6...?

Please explain y not, thank you.


I think what defenestrate is trying to get at is the fact that 6/6 is just 1, i.e. doesn't matter what number we get in the first roll. What we are concerned with is the fact that this number not show up again, hence starting with 5/6 (the prob of 2nd roll) and so on and so forth. In the case of 6 rolls, the last roll has a prob of 1/6 [5/6*4/6*3/6*2/6*1/6] = 5!/6^5 which is the same as 6!/6^6 if you put 6/6 as the first roll instead of 1.

In the case of 5 rolls, the last roll has a prob of 2/6 [5/6*4/6*3/6*2/6]= 5!/6^4 which is the same as 6!/6^5 if you put 6/6 as the first roll instead of 1.

Additionally, for the sake of completeness, the prob of 5 dice is [1- (120/1296)] = 49/54 not 8/9.
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 573
Followers: 1

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

GMAT Tests User
 [#permalink] New post 11 Oct 2007, 02:21
Skewed,

Thank you for making it clear, really appreciate.
Manager
Manager
User avatar
Joined: 07 Sep 2007
Posts: 121
Followers: 1

Kudos [?]: 9 [0], given: 0

 [#permalink] New post 11 Oct 2007, 08:11
Skewed wrote:
Additionally, for the sake of completeness, the prob of 5 dice is [1- (120/1296)] = 49/54 not 8/9.


Whoops, must have made a careless error. =)
Intern
Intern
User avatar
Joined: 02 Aug 2007
Posts: 38
Followers: 0

Kudos [?]: 7 [0], given: 0

Re: PERMUTATION & COMBINATION gurus!!! [#permalink] New post 12 Oct 2007, 01:53
IrinaOK wrote:
6 fair dice are tossed. What is the probability that at least two of them show the same face.


Pleas provide your explanations, thank you.

original post available at:

http://www.gmatclub.com/forum/t53592


I found this post about 2 years old and it makes reference to the OA answer:
http://www.gmatclub.com/forum/t21471

OA says (0.985) which makes (1 - 6!/6^6) correct.
Re: PERMUTATION & COMBINATION gurus!!!   [#permalink] 12 Oct 2007, 01:53
    Similar topics Author Replies Last post
Similar
Topics:
6 fair dice are tossed. What is the probability that at young_gun 7 08 Oct 2007, 11:25
3 A fair coin is tossed 5 times. What is the probability that netcaesar 9 24 May 2006, 22:30
In tossing 4 fair dice, what is the probability of tossing, cloaked_vessel 10 27 Oct 2005, 17:56
6 fair dice are tossed. What is the probability that at cloaked_vessel 2 16 Oct 2005, 17:45
A fair coin is tossed 6 times . what is the probability that rxs0005 9 16 Jan 2005, 17:39
Display posts from previous: Sort by

6 fair dice are tossed. What is the probability that at

  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®.