January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

VP
Joined: 16 Jul 2009
Posts: 1019
Schools: CBS
WE 1: 4 years (Consulting)

Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
05 Nov 2009, 13:41
Question Stats:
50% (01:21) correct 50% (02:27) wrong based on 405 sessions
HideShow timer Statistics
Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? A. 24/64 B. 32/64 C. 36/64 D. 40/64 E. 42/64
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The sky is the limit 800 is the limit
GMAT Club Premium Membership  big benefits and savings




Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
05 Nov 2009, 13:59
noboru wrote: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2. P=1/2.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 22 Jun 2010
Posts: 106

Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
24 Sep 2010, 11:17
would you love to see how attacked it? if Joe is expected to outscore his friend, he should get these sums, 11,12,13...18 all possibilities are from 3 to 18 so : prob =8/16 equal to 1/2 PS. If you are wondering how I came to 3 as min because 1+1+1 and likewise 18 is max (6+6+6) Edit: NOTE THE ABOVE SOLUTION IS NOT CORRECT. SEE POST BELOW




Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
24 Sep 2010, 22:20
imania wrote: would you love to see how attacked it? if Joe is expected to outscore his friend, he should get these sums, 11,12,13...18 all possibilities are from 3 to 18 so : prob =8/16 equal to 1/2 PS. If you are wondering how I came to 3 as min because 1+1+1 and likewise 18 is max (6+6+6) Unfortunately this approach is not right though for this particular case it gave a correct answer. Consider this: if it were that Mary scored not 10 but 17 then Joe to outscore Mary should get only 18 and according to your approach as there are total of 16 scores possible then the probability of Joe getting 18 would be 1/16. But this is not correct, probability of 18 is (1/6)^3=1/216 not 1/16. This is because not all scores from 3 to 18 have equal # of ways to occur: you can get 10 in many ways but 3 or 18 only in one way (3=1+1+1 and 18=6+6+6). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



VP
Joined: 16 Jul 2009
Posts: 1019
Schools: CBS
WE 1: 4 years (Consulting)

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
25 Sep 2010, 04:37
Bunuel wrote: imania wrote: would you love to see how attacked it? if Joe is expected to outscore his friend, he should get these sums, 11,12,13...18 all possibilities are from 3 to 18 so : prob =8/16 equal to 1/2 PS. If you are wondering how I came to 3 as min because 1+1+1 and likewise 18 is max (6+6+6) Unfortunately this approach is not right though for this particular case it gave a correct answer. Consider this: if it were that Mary scored not 10 but 17 then Joe to outscore Mary should get only 18 and according to your approach as there are total of 16 scores possible then the probability of Joe getting 18 would be 1/16. But this is not correct, probability of 18 is (1/6)^3=1/216 not 1/16. This is because not all scores from 3 to 18 have equal # of ways to occur: you can get 10 in many ways but 3 or 18 only in one way (3=1+1+1 and 18=6+6+6). Hope it's clear. Fantastic explanation!
_________________
The sky is the limit 800 is the limit
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 19 Apr 2010
Posts: 176
Schools: ISB, HEC, Said

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
27 Sep 2010, 03:01
Is there any alternate approach to solve this problme?



Retired Moderator
Joined: 02 Sep 2010
Posts: 765
Location: London

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
27 Sep 2010, 14:55
Yes, but alternative approaches revolve around the same idea. I can tell you how to reduce this problem to that of a multinomial expansion if you want, but the technique is beyond the scope of GMAT. The answer presented here is the simplest possible
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 05 Oct 2010
Posts: 1

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
05 Oct 2010, 22:05
How did you get the possible scores i.e 16 and so the probablity is 1/16 Bunuel wrote: imania wrote: Unfortunately this approach is not right though for this particular case it gave a correct answer.
Consider this: if it were that Mary scored not 10 but 17 then Joe to outscore Mary should get only 18 and according to your approach as there are total of 16 scores possible then the probability of Joe getting 18 would be 1/16. But this is not correct, probability of 18 is (1/6)^3=1/216 not 1/16.
This is because not all scores from 3 to 18 have equal # of ways to occur: you can get 10 in many ways but 3 or 18 only in one way (3=1+1+1 and 18=6+6+6).
Hope it's clear.



Retired Moderator
Joined: 02 Sep 2010
Posts: 765
Location: London

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
05 Oct 2010, 23:26
sanober1985 wrote: How did you get the possible scores i.e 16 and so the probablity is 1/16 Bunuel wrote: imania wrote: Unfortunately this approach is not right though for this particular case it gave a correct answer.
Consider this: if it were that Mary scored not 10 but 17 then Joe to outscore Mary should get only 18 and according to your approach as there are total of 16 scores possible then the probability of Joe getting 18 would be 1/16. But this is not correct, probability of 18 is (1/6)^3=1/216 not 1/16.
This is because not all scores from 3 to 18 have equal # of ways to occur: you can get 10 in many ways but 3 or 18 only in one way (3=1+1+1 and 18=6+6+6).
Hope it's clear. The possible scores are {3,4,5,...,18} which is 16 distinct numbers But probability is NOT 1/16. The outcomes are not equally likely
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
06 Oct 2010, 02:46
sanober1985 wrote: How did you get the possible scores i.e 16 and so the probablity is 1/16 Bunuel wrote: imania wrote: Unfortunately this approach is not right though for this particular case it gave a correct answer.
Consider this: if it were that Mary scored not 10 but 17 then Joe to outscore Mary should get only 18 and according to your approach as there are total of 16 scores possible then the probability of Joe getting 18 would be 1/16. But this is not correct, probability of 18 is (1/6)^3=1/216 not 1/16.
This is because not all scores from 3 to 18 have equal # of ways to occur: you can get 10 in many ways but 3 or 18 only in one way (3=1+1+1 and 18=6+6+6).
Hope it's clear. When you roll 3 dice you can have the following sums: 3 (min possible 1+1+1), 4, 5, 6, ...., 18 (max possible 6+6+6), so total of 16 possible sums. But as you can see in my previous post (the one you quote) the probability of these score are not equal, so it's not 1/16 for each. devashish wrote: Bunuel wrote: noboru wrote: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2. P=1/2. Amazing explanation, but is this a GMAT type question, if yes then I doubt I will ever be able to solve such questions in Real GMAT Time and space. It is too far fetched for me to even think I can crack such a question in normal finite time, forget GMAT Time !!! Don't worry, you won't see such kind of question on GMAT.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 30 Nov 2010
Posts: 213
Schools: UC Berkley, UCLA

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
31 Jan 2011, 16:23
How were you able to come up with (1+2+3+4+5+6)? I understand that one outcome out of six occurs when Joe rolls the dice but the other part... a bit puzzling???
_________________
Thank you for your kudoses Everyone!!!
"It always seems impossible until its done." Nelson Mandela



Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
31 Jan 2011, 16:36



VP
Joined: 02 Jul 2012
Posts: 1169
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
03 Jul 2012, 23:05
Bunuel wrote: noboru wrote: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2. P=1/2. Can someone please explain what mistake i'm doing: Total No. Of Possible Outcomes = 216 Outcomes where Joe scores 10 or less: 111 > 1 222 > 1 333 > 1 112 > 3, 113 > 3, 114 > 3, 115 > 3, 116 > 3, 221 > 3, 223 > 3, 224 > 3, 225 > 3, 226 > 3, 331 > 3, 332 > 3, 334 > 3, 441 > 3, 442 > 3, Adding everything up = 48 Outcomes where Joe scores more than 10 = 216  48 = 168 Probability = 168/216 = 7/9
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
04 Jul 2012, 00:11
MacFauz wrote: Bunuel wrote: noboru wrote: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5. Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2. P=1/2. Can someone please explain what mistake i'm doing: Total No. Of Possible Outcomes = 216 Outcomes where Joe scores 10 or less: 111 > 1 222 > 1 333 > 1 112 > 3, 113 > 3, 114 > 3, 115 > 3, 116 > 3, 221 > 3, 223 > 3, 224 > 3, 225 > 3, 226 > 3, 331 > 3, 332 > 3, 334 > 3, 441 > 3, 442 > 3, Adding everything up = 48 Outcomes where Joe scores more than 10 = 216  48 = 168 Probability = 168/216 = 7/9 You are missing some cases: 123  6 ways; 124  6 ways; 125  6 ways; 126  6 ways; 134  6 ways; 135  6 ways; 136  6 ways; 145  6 ways; 234  6 ways; 235  6 ways. So, total of 60 scenarios were missing. Together with the 48 cases you counted we would have 48+60=108 ways to get the sum of 10 or less, so the probability is 1108/216=1/2. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 28 Dec 2012
Posts: 102
Location: India
Concentration: Strategy, Finance
WE: Engineering (Energy and Utilities)

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
05 Jan 2013, 05:56
Joe should score 11,12... 17,18 to score over mary. Now lets consider 1 by 1: 18: 6,6,6 combination > 1 arrangement 18 > 1 possibility 17: 6,6,5 combination > 3 arrangement 17 > 3 possibilities 16: 6,6,4 combination > 3 arrangement 6,5,5 combination > 3 arrangement 16 > 6 possibilities 15: 6,6,3 combination > 1 arrangement 6,5,4 combination > 6 arrangement 5,5,4 combination > 3 arrangement 15 > 10 possibilities similarly for 14,13,12,and 11 we have 15,21,25,27 possibilities respectively. Total favorable: 1+3+6+10+15+21+25+27 = 108 possibilities Probability = 108/(6*6*6) = 1/2 or 32/64 Two important points... the solution is not the shortest but shows systematic listing method useful for other questions. Secondly, It appeared as though a series was forming.. which is not the case!!! Kudos for the Solution plz....
_________________
Impossibility is a relative concept!!



Intern
Joined: 29 Apr 2014
Posts: 3

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
29 May 2014, 22:10
Hi Bunuel, Can you please explain your answer of (1/6)^3 = 1/216 in case mary scores 17.



Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
30 May 2014, 00:31



Intern
Joined: 24 Jan 2015
Posts: 1

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
07 Mar 2015, 00:31
What would be the approach to be followed if the question asked is to find the probability of Joe hitting more than 15??



Math Expert
Joined: 02 Sep 2009
Posts: 52428

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
07 Mar 2015, 04:35



Manager
Joined: 02 Jan 2016
Posts: 124

Re: Mary and Joe are to throw three dice each. The score is the
[#permalink]
Show Tags
28 Oct 2018, 04:39
BunuelThe way I did this: values greater than 10 are 11,12,13,14,15,16,17,18. i.e 8 values so, 8/18 (18 is the maximum Value of all three dices), so 8/18 *4/4 = 32/64. Is this correct ?




Re: Mary and Joe are to throw three dice each. The score is the &nbs
[#permalink]
28 Oct 2018, 04:39



Go to page
1 2
Next
[ 22 posts ]



