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

It is currently 19 Apr 2014, 22:23

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

Hard probability problem: 2 dice sum of 3 BEFORE sum of 7

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
Joined: 15 Apr 2010
Posts: 48
Followers: 0

Kudos [?]: 14 [0], given: 10

Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 06 Oct 2010, 00:21
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
Anyone has idea about this?

You have two dice, what is the probability of rolling a sum of 3 BEFORE rolling a sum of 7?

Thanks..
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 74

Kudos [?]: 394 [0], given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 06 Oct 2010, 00:47
catennacio wrote:
Anyone has idea about this?

You have two dice, what is the probability of rolling a sum of 3 BEFORE rolling a sum of 7?

Thanks..


Can you define the problem more precisely ?

You start rolling the dice, and the sum of two dice is 3, but the third dice adds up to a 7 ?

Or do u roll three dice twice, and the first time you get a 3 and the second time a 7 ?
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18405 [1] , given: 2350

GMAT Tests User CAT Tests
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 06 Oct 2010, 02:39
1
This post received
KUDOS
Expert's post
catennacio wrote:
Anyone has idea about this?

You have two dice, what is the probability of rolling a sum of 3 BEFORE rolling a sum of 7?

Thanks..


First of all please note that this question is far beyond the GMAT scope.

P(sum=3)=\frac{2}{36}=\frac{1}{18}: either (1,2) or (2,1) out of total of 36 different combinations of two dice;

P(sum=7)=\frac{6}{36}=\frac{1}{6}: (1,6), (2,5), (3,4), (4,3), (5,2), or (6,1);

P(other \ sum)=1-(\frac{1}{18}+\frac{1}{6})=\frac{7}{9}, probability of sums: 4, 5, 6, 8, 9, 10, 11, and 12;

Winning scenarios:
{sum=3} - we have sum of 3 on the first roll of two dice - P_1=\frac{1}{18};
{other sum; sum=3} - on the first roll we have other sum and sum of 3 on the second roll - P_2=\frac{7}{9}*\frac{1}{18};
{other sum; other sum; sum=3} - P_3=(\frac{7}{9})^2*\frac{1}{18};
{other sum; other sum; other sum; sum=3} - P_4=(\frac{7}{9})^3*\frac{1}{18};
...

So probability of rolling a sum of 3 BEFORE rolling a sum of 7 would be the sum of the above infinite series:
P=\frac{1}{18}+\frac{7}{9}*\frac{1}{18}+(\frac{7}{9})^2*\frac{1}{18}+(\frac{7}{9})^3*\frac{1}{18}+...=\frac{1}{18}(1+\frac{7}{9}+(\frac{7}{9})^2+(\frac{7}{9})^3+...)=\frac{1}{18}(1+\frac{\frac{7}{9}}{1-\frac{7}{9}})=\frac{1}{18}(1+\frac{7}{2})=\frac{1}{4} (for geometric progression with common ratio |q|<1, the sum of the progression: b_1, b_2, ... is Sum=\frac{b_1}{1-q}.).

OR:

As P(sum=3)=\frac{2}{36} and P(sum=7)=\frac{6}{36} then getting the sum of 7 is 3 times more likely than getting the sum of 3, so the sum of 3 has 1 chance out of 4 to get first out of any number of tries, so P=\frac{1}{4} or P=\frac{\frac{2}{36}}{\frac{2}{36}+\frac{6}{36}}=\frac{1}{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

Manager
Manager
Joined: 25 Jun 2010
Posts: 94
Followers: 1

Kudos [?]: 22 [0], given: 0

GMAT ToolKit User GMAT Tests User
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 06 Oct 2010, 04:29
Excellently done Bunuel!

Posted from my mobile device Image
Intern
Intern
Joined: 15 Apr 2010
Posts: 48
Followers: 0

Kudos [?]: 14 [0], given: 10

Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 06 Oct 2010, 15:42
Thank you very much Buneul for your answer. However I have a few questions:

I understand up to P(other sum). How can you conclude the winning scenario is other sum then sum 3? I know it's a possible case, but why is it (other sum, sum 3) will lead to a (other sum, sum 3, then sum 7). It could be (other sum, sum 3, sum 8) - after 3 rollings, while what we expect is sum 7. Therefore the (other sum, other sum,..., sum 3) could be a wrong case.

On the other hand, if we can conclude other sum, other sum,..., sum 3 is a winning scenario, have we assume the probability of sum 7 and other sum but not 7 are the same, while there are different?

I don't understand this sentence too "So probability of rolling a sum of 3 BEFORE rolling a sum of 7 would be the sum of the above infinite series" - how can you conclude it's the sum that series, how about if we have an AFTER word? What is the difference between BEFORE and AFTER?

Edit: I like your second approach, by comparing the fraction of the probability of 2 events we can say P = 1/4, but I still don't understand the word BEFORE.. What if they ask for AFTER? Will we still compare the 2 probabilities?
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18405 [0], given: 2350

GMAT Tests User CAT Tests
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 07 Oct 2010, 02:12
Expert's post
catennacio wrote:
Thank you very much Buneul for your answer. However I have a few questions:

I understand up to P(other sum). How can you conclude the winning scenario is other sum then sum 3? I know it's a possible case, but why is it (other sum, sum 3) will lead to a (other sum, sum 3, then sum 7). It could be (other sum, sum 3, sum 8) - after 3 rollings, while what we expect is sum 7. Therefore the (other sum, other sum,..., sum 3) could be a wrong case.

On the other hand, if we can conclude other sum, other sum,..., sum 3 is a winning scenario, have we assume the probability of sum 7 and other sum but not 7 are the same, while there are different?

I don't understand this sentence too "So probability of rolling a sum of 3 BEFORE rolling a sum of 7 would be the sum of the above infinite series" - how can you conclude it's the sum that series, how about if we have an AFTER word? What is the difference between BEFORE and AFTER?

Edit: I like your second approach, by comparing the fraction of the probability of 2 events we can say P = 1/4, but I still don't understand the word BEFORE.. What if they ask for AFTER? Will we still compare the 2 probabilities?


When we roll 2 dice the sum can be 3, 7, or some other number (not 3 and not 7). The questions asks for the cases when we get the sum of 3 BEFORE the sum of 7.

For example why the cases I wrote are the winning scenarios:
{sum=3} - means that right on the first throw we have sum of 3, so we have 3 before 7 (as no 7 at all);
{other sum; sum=3} - first roll not 7 and not 3, so we can continue. On the second throw we have sum of 3, so again 3 before 7 - OK;
{other sum; other sum; sum=3} - sum of 3 on the third roll;
{other sum; other sum; other sum; sum=3} - sum of 3 on the fourth roll;
....
{other sum; other sum; other sum; ..., other sum on the nth roll; sum of 3 on the (n+1)th roll} - out of n+1 rolls we have other sum for the rolls from 1 to n and sum of 3 on the (n+1)th roll, still 3 before 7 - OK;
...

The above can be continued infinitely, and all above case represent the scenario when we have the sum of 3 BEFORE we have the sum of 7 (which will eventually occur on some roll afterwards). So the probability of getting 3 before 7 would be the sum of the probabilities of the above events.

Hope it's clear. Anyway: you won't need this for GMAT, so don't worry too much.
_________________

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

Intern
Intern
Joined: 15 Apr 2010
Posts: 48
Followers: 0

Kudos [?]: 14 [0], given: 10

Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 07 Oct 2010, 03:28
Thanks Bunuel now I understand it. However I think you miss the scenario where sum=7 occurs before sum=3. For example, 1st time sum=7, 2nd time sum=3, so the probability must be 6/36 * 2/36. You assumed that sum 7 never happens before sum 3 so you take the probability of other sum (7/9) to calculate. Am I wrong?
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18405 [0], given: 2350

GMAT Tests User CAT Tests
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 07 Oct 2010, 04:38
Expert's post
catennacio wrote:
Thanks Bunuel now I understand it. However I think you miss the scenario where sum=7 occurs before sum=3. For example, 1st time sum=7, 2nd time sum=3, so the probability must be 6/36 * 2/36. You assumed that sum 7 never happens before sum 3 so you take the probability of other sum (7/9) to calculate. Am I wrong?


Yes, you are wrong. I'm not assuming that 7 doesn't occur before 3 rather than I'm only interested to count the probability of the cases when 3 occur before 7 as this is what the question is asking, that's why I'm not considering the cases when 7 occur before 3.
_________________

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

Manager
Manager
Joined: 27 May 2008
Posts: 127
Followers: 2

Kudos [?]: 21 [0], given: 4

Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 07 Oct 2010, 22:40
Nice explanation Bunuel !
Intern
Intern
Joined: 15 Apr 2010
Posts: 48
Followers: 0

Kudos [?]: 14 [0], given: 10

Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7 [#permalink] New post 08 Oct 2010, 18:11
Thanks Bunuel, you're right.. sometimes I got off the track when thinking... thanks for being patient with me :)
Re: Hard probability problem: 2 dice sum of 3 BEFORE sum of 7   [#permalink] 08 Oct 2010, 18:11
    Similar topics Author Replies Last post
Similar
Topics:
New posts Two dice are rolled. What is the probability the sum will be sperumba 7 26 Jan 2006, 17:38
New posts Two dice are rolled. What is the probability the sum will be Cedars 2 16 Oct 2006, 16:42
New posts What is the probability that the sum of two dice will yield sez780 3 03 Jul 2008, 05:44
New posts 1 Experts publish their posts in the topic What is the probability that the sum of two dice will yield Paradox69 2 08 Feb 2012, 13:50
This topic is locked, you cannot edit posts or make further replies. New 7 Experts publish their posts in the topic A and B in turns, throw a dice. If A gets a sum of 8 before PiyushK 3 08 Aug 2013, 06:27
Display posts from previous: Sort by

Hard probability problem: 2 dice sum of 3 BEFORE sum of 7

  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®.