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

It is currently 12 Jul 2014, 17:48

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

In a game, one player throws two fair, six-sided die at the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
avatar
Joined: 14 Feb 2013
Posts: 33
Schools: Duke '16
Followers: 0

Kudos [?]: 13 [2] , given: 14

In a game, one player throws two fair, six-sided die at the [#permalink] New post 01 May 2013, 10:03
2
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (medium)

Question Stats:

36% (02:34) correct 63% (01:29) wrong based on 129 sessions
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?

A. 1/3
B. 4/9
C. 5/9
D. 2/3
E. 3/4
[Reveal] Spoiler: OA

_________________

Consider giving +1 Kudo :) when my post helps you.
Also, Good Questions deserve Kudos..!

Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [0], given: 16

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 01 May 2013, 10:40
Option C.

the number of cases in which he can lose the game are when both the faces have neither of 5 or 1 or both. so the possible combinations are (2,2),(2,3),(2,4) (2,6) and 12 more with 3,4,6.

probability of loss = # loss cases/# total no of cases
= 16/36 or 4/9

hence probability of win = 1-p(loss). = 1-(4/9) = 5/9
2 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 101

Kudos [?]: 1063 [2] , given: 219

GMAT ToolKit User GMAT Tests User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 01 May 2013, 10:41
2
This post received
KUDOS
We have 2 good (read five and one) possibilities (G) on 6 faces G=2/6 and 4 bad possibilities (B) on 6 faces B=4/6
The winning combinations are the ones with at least a G in it so:
G,B
B,G
G,G

G,B and B,G have the same probability \frac{2}{6}*\frac{4}{6}=\frac{2}{9} each
G,G has a probability of \frac{2}{6}*\frac{2}{6}=\frac{1}{9}
Sum them up \frac{2}{9}+\frac{2}{9}+\frac{1}{9}=\frac{5}{9}
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18514
Followers: 3193

Kudos [?]: 21347 [5] , given: 2546

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 02 May 2013, 03:24
5
This post received
KUDOS
Expert's post
karishmatandon wrote:
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?

A. 1/3
B. 4/9
C. 5/9
D. 2/3
E. 3/4


Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:

P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.

Answer: C.
_________________

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 02 Sep 2012
Posts: 292
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 3

Kudos [?]: 61 [0], given: 99

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 05 May 2013, 04:59
Zarrolou wrote:
We have 2 good (read five and one) possibilities (G) on 6 faces G=2/6 and 4 bad possibilities (B) on 6 faces B=4/6
The winning combinations are the ones with at least a G in it so:
G,B
B,G
G,G

G,B and B,G have the same probability \frac{2}{6}*\frac{4}{6}=\frac{2}{9} each
G,G has a probability of \frac{2}{6}*\frac{2}{6}=\frac{1}{9}
Sum them up \frac{2}{9}+\frac{2}{9}+\frac{1}{9}=\frac{5}{9}


WHy in both winning combination we are calculating for GG only once .
May be on first die 5 and second die one or on first die one and second die 5...These can combinations can also occur na? ..WHy we are not considering this scenario?
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 101

Kudos [?]: 1063 [1] , given: 219

GMAT ToolKit User GMAT Tests User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 05 May 2013, 05:43
1
This post received
KUDOS
skamal7 wrote:
WHy in both winning combination we are calculating for GG only once .
May be on first die 5 and second die one or on first die one and second die 5...These can combinations can also occur na? ..WHy we are not considering this scenario?


Hi skamal7,

Consider the following example that will explain better than any theoretical information.
You say that G,G should be counted twice, so the possible combinations are:

G,G=1/9
G,G=1/9
B,G=2/9
G,B=2/9
B,B=4/9
[ also if your method is correct B,B should be counted twice =4/9 ]

don't you see anything odd? The sum of the probability of each case is greater than 1! \frac{1+1+2+2+4}{9}=\frac{10}{9}
[ if you count B,B twice it becomes \frac{14}{9} ]

Why does this happen?Let's look at the theory now
The formula to solve this problem is (nCk)p^k*q^{(n-k)} where p=1/3 and q=2/3 and N are the dies and K are the good outcomes:

Case two good (2C2)(\frac{1}{3})^2(\frac{2}{3})^0=\frac{1}{9}
Case one good one bad (2C1)(\frac{1}{3})^1(\frac{2}{3})^1=\frac{4}{9}
Case two bad (2C0)(\frac{1}{3})^0(\frac{2}{3})^2=\frac{4}{9}

Tot sum = \frac{1+4+4}{9}=1

Hope it's clear now, let me know
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

1 KUDOS received
Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 12 [1] , given: 1

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 05 May 2013, 08:09
1
This post received
KUDOS
karishmatandon wrote:
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?

A. 1/3
B. 4/9
C. 5/9
D. 2/3
E. 3/4



Instead of trying to count the overlapping events and thereby complicating the probability calculation, we can simply calculate the probability of 'not winning' and subtract it from 1 to get the probability of 'winning'

Therefore required probability P = 1 - (\frac{4}{6})*(\frac{4}{6})

P = \frac{5}{9}

Correct option is C :)
Senior Manager
Senior Manager
avatar
Joined: 02 Sep 2012
Posts: 292
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 3

Kudos [?]: 61 [0], given: 99

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 05 May 2013, 08:19
Zarollu,
Unfortunately GMATCLUB doesn't allow me to reward you with more than 1 kudos :( .. Thanks for such an awesome explainanation
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Intern
Intern
avatar
Joined: 10 Mar 2012
Posts: 37
GMAT 1: 730 Q47 V44
Followers: 0

Kudos [?]: 11 [0], given: 12

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 06 May 2013, 10:03
I think the question should be re-worded. 'At least a five' sounds like >= 5. Therefore, my result was 1-(1/2*1/2) = 3/4
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 22 Mar 2013
Posts: 665
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 109 [0], given: 111

Premium Member CAT Tests
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 30 Jul 2013, 10:51
I also got confused with this at least, i interpreted it as 5-x 6-x 1-x 5-1 6-1 vice-versa cases.
_________________

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: WOULD: when to use?

Intern
Intern
avatar
Joined: 25 Jun 2013
Posts: 12
Followers: 0

Kudos [?]: 12 [0], given: 2

GMAT ToolKit User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 30 Jul 2013, 13:47
I too got confused with the word "at least" I assumed that either a 1, 5 or 6 would constitute a win. Hmmm
Manager
Manager
User avatar
Joined: 24 Nov 2012
Posts: 161
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 12

Kudos [?]: 57 [0], given: 73

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 03 Aug 2013, 03:10
dyaffe55 wrote:
I think the question should be re-worded. 'At least a five' sounds like >= 5. Therefore, my result was 1-(1/2*1/2) = 3/4


I made the same mistake as well... But for the condition above wouldnt the answer be 5/6?

Bunuel/Zarroulou could you confirm? If a win was 1,5,6 instead of 1 and 5?
_________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

http://www.manhattangmat.com/blog/index ... nprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 101

Kudos [?]: 1063 [0], given: 219

GMAT ToolKit User GMAT Tests User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 03 Aug 2013, 03:15
Transcendentalist wrote:
dyaffe55 wrote:
I think the question should be re-worded. 'At least a five' sounds like >= 5. Therefore, my result was 1-(1/2*1/2) = 3/4


I made the same mistake as well... But for the condition above wouldnt the answer be 5/6?

Bunuel/Zarroulou could you confirm? If a win was 1,5,6 instead of 1 and 5?


If the question were "at least one five" (only five, and not also six to win), then yes the answer would be 1-5/6*5/6.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Manager
Manager
User avatar
Joined: 24 Nov 2012
Posts: 161
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 12

Kudos [?]: 57 [0], given: 73

Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 03 Aug 2013, 03:52
I meant the condition for a win was at least a five (5 or 6) or 1 on either die...
_________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

http://www.manhattangmat.com/blog/index ... nprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 101

Kudos [?]: 1063 [0], given: 219

GMAT ToolKit User GMAT Tests User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 03 Aug 2013, 04:21
Transcendentalist wrote:
I meant the condition for a win was at least a five (5 or 6) or 1 on either die...


Yes, with 5 or 6 the probability is 1-4/6*4/6
With only five the probability is 1-5/6*5/6
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 128 [0], given: 254

GMAT ToolKit User
Re: In a game, one player throws two fair, six-sided die at the [#permalink] New post 23 Mar 2014, 16:14
Question is not clear when it refers to 'at least' does it refer to at least a 5, that meaning 5 or 6? Or does it refer to have at least one of two: either a 5 or a 1?

Is it clear to everyone else?

Cheers
J
Re: In a game, one player throws two fair, six-sided die at the   [#permalink] 23 Mar 2014, 16:14
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Brian plays a game in which two fair, six-sided dice are rol sidinsin 6 18 Jun 2014, 07:52
2 Experts publish their posts in the topic A magician holds one six-sided die in his left hand and two carcass 9 15 May 2012, 16:52
In a game with one die, player X wins if the number of andrehaui 1 24 Apr 2007, 04:19
2 players each throw one fair die. In order to win, player A Paul 7 11 Nov 2004, 17:53
If a fair six-sided die is rolled three times, what is the Bhai 2 11 Sep 2004, 08:14
Display posts from previous: Sort by

In a game, one player throws two fair, six-sided die at the

  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®.