|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 04 Feb 2004
Posts: 29
Location: USA
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Mary and Joe throw three dice each. If Mary gets 10, what [#permalink]
 04 Apr 2005, 14:08
Question Stats:
0% (00:00) correct
100% (03:19) wrong based on 1 sessions
Mary and Joe throw three dice each. If Mary gets 10, what is the probability that Joe will outscore Mary? OPEN DISCUSSION OF THIS QUESTION IS HERE: mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-86407.html AND HERE: mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
|
|
|
|
|
|
|
|
|
Director
Joined: 19 Feb 2005
Posts: 508
Location: Milan Italy
Followers: 1
Kudos [?]:
2
[0], given: 0
|
1/4
my formulas are too lengthy to be those you should actually use to solve this, so I'm waiting for other people to answer. (provided that my answer is correct!)
|
|
|
|
|
|
Intern
Joined: 04 Feb 2004
Posts: 29
Location: USA
Followers: 0
Kudos [?]:
0
[0], given: 0
|
that is incorrect, the correct answer is 1/2...any ideas how to get to that?
|
|
|
|
|
|
Director
Joined: 19 Feb 2005
Posts: 508
Location: Milan Italy
Followers: 1
Kudos [?]:
2
[0], given: 0
|
rc1979 wrote: that is incorrect, the correct answer is 1/2...any ideas how to get to that?
damn! this is not testing our knowledge of permutations/combinations/possible outcomes
I couldn't be more stupid
Follow this:
expected value of a dice= 3.5
expected value of 3 ones= 10.5
so we have 1/2 to score less than 10.5 and 1/2 to score more than 10.5
|
|
|
|
|
|
Director
Joined: 19 Feb 2005
Posts: 508
Location: Milan Italy
Followers: 1
Kudos [?]:
2
[0], given: 0
|
gmat2me2 wrote: rc1979 wrote: Mary and Joe throw three dice each. If Mary gets 10, what is the probability that Joe will outscore Mary? How to do this in a concise way? see above 
|
|
|
|
|
|
Director
Joined: 18 Feb 2005
Posts: 720
Followers: 1
Kudos [?]:
2
[0], given: 0
|
thearch wrote: gmat2me2 wrote: rc1979 wrote: Mary and Joe throw three dice each. If Mary gets 10, what is the probability that Joe will outscore Mary? How to do this in a concise way? see above :-D Thanks but can you explain how you got 3.5 for 1 dice ?
|
|
|
|
|
|
Director
Joined: 19 Feb 2005
Posts: 508
Location: Milan Italy
Followers: 1
Kudos [?]:
2
[0], given: 0
|
expected value results from the sum of probability*value (it is an aleatory number)
in this case:
1/6*1+1/6*2+1/6*3+1/6*4+1/6*5+1/6*6=1/6*(1+2+3+4+5+6)=3.5
another example could be
we have 5 bottles of wine that are sold in a supermarket
2 of type A
2 of type B
1 of type C
bottles of type A are charged $5 each
bottles of type B are charged $10 each
bottles of type C are charged $15 each
John buys a bottle. If John doesn't know what bottle he chose, how much should he expect to pay?
EV=2/5*$5+2/5*$10+1/5*$15=$9
don't know if I'm clear with my English. please correct me if my reasoning is wrong
|
|
|
|
|
|
Director
Joined: 31 Aug 2004
Posts: 619
Followers: 1
Kudos [?]:
8
[3] , given: 0
|
3
This post received
KUDOS
Proba is 1/2 just because we are half way from 18.
From 3 (minimum score) to 10 there is a 7 range
from 11 (minimum score to outscore) to 18 (max) you have a 7 range.
So Prob to score 11 = Prob to score 10
Prob 9 = Prob 12
...
|
|
|
|
|
|
VP
Joined: 13 Jun 2004
Posts: 1134
Location: London, UK
Schools: Tuck'08
Followers: 5
Kudos [?]:
14
[1] , given: 0
|
1
This post received
KUDOS
1/2
min result : 3 (1+1+1)
max result : 18 (6+6+6)
number of outcomes : 18-3+1 = 16
We want outcome >10 and max is 18 so there are 8 possibilities over 16
8/16 = 1/2
|
|
|
|
|
|
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 10
Kudos [?]:
158
[0], given: 0
|
Good Antmavel!
Total possible values are from 3-18, therefore 16 outcomes.
Desired outcomes are from 11-18, therefore 8 outcomes.
Possibility is 8/16=1/2.
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
|
|
|
|
|
|
Director
Joined: 12 Jul 2007
Posts: 875
Followers: 8
Kudos [?]:
138
[1] , given: 0
|
1
This post received
KUDOS
bmwhype2 wrote: Antmavel wrote: 1/2
min result : 3 (1+1+1)
max result : 18 (6+6+6)
number of outcomes : 18-3+1 = 16
We want outcome >10 and max is 18 so there are 8 possibilities over 16
8/16 = 1/2 whats the logic behind that equation? 3 dice: lowest number possible 1+1+1 =3, greatest number possible 6+6+6=18
18-3+1 (because inclusive) = 16 possible outcomes. 8 of which are greater than 10
|
|
|
|
|
|
Manager
Joined: 22 Jul 2008
Posts: 156
Followers: 1
Kudos [?]:
5
[0], given: 0
|
There is no need for any calculations here. No matter what the numbers are, the probability will always be 1/2. The reason for that is that Joe can have only 2 outcomes- either outscore Mary or be outscored. Simple, isn't it! It would have been a different question if it was required to find out probability of Joe getting a particular score.
|
|
|
|
|
|
SVP
Joined: 07 Nov 2007
Posts: 1837
Location: New York
Followers: 20
Kudos [?]:
297
[0], given: 5
|
KASSALMD wrote: There is no need for any calculations here. No matter what the numbers are, the probability will always be 1/2. The reason for that is that Joe can have only 2 outcomes- either outscore Mary or be outscored. Simple, isn't it! It would have been a different question if it was required to find out probability of Joe getting a particular score. In this case calculations are not required. because possible outcomes for sum >10 equal to possible coutcomes for sum <=10What if question is changed to . Mary and Joe throw three dice each. If Mary gets 8, what is the probability that Joe will outscore Mary? Definitely you need to calculate.
_________________
Your attitude determines your altitude
Smiling wins more friends than frowning
|
|
|
|
|
|
Intern
Joined: 06 Jun 2009
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Guys can u explain the Ist question( Probability ) wat i did is as follows Total no cases= 6*6*6= 216 Favourable no of cases= any no greater than 10 till 18 that is 11 12 13 14 15 16 17 18= 8 so pro= 8/216= 1/27 is it ok? 
|
|
|
|
|
|
Manager
Joined: 14 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 3
Kudos [?]:
18
[0], given: 1
|
rc1979 wrote: Mary and Joe throw three dice each. If Mary gets 10, what is the probability that Joe will outscore Mary? Assuming D6 6*6*6 VALUES in total What's Pr (sum>10?) What's 1-Pr(sum<8)? 1<=X<=6 1<=Y<=6 1<=Z<=6 X+Y+Z < 8 |{X,Y,Z}|? Let's calculate Pr(sum<8): Say X=1 Then Y+Z<7? 1/5 1/4 1/3 1/2 1/1 2/4 2/3 2/2 2/1 3/3 3/2 3/1 4/2 4/1 5/1 (15 values) Say X=2 Then Y+Z<6? 4/1 3/2 3/1 2/3 2/2 2/1 1/4 1/3 1/2 1/1 (10 values) say x=3 Then Y+Z<5? 3/1 2/2 2/1 1/3 1/2 1/1 (6 values) say x=4 Then Y+Z<4? 2/1 1/2 1/1 (3 values) say x=5 Then Y+Z<3? 1/1 (1 value) say x=6? then Y+Z<2? (0 values) In total: 15+10+6+3+1+0 = 35/216 1-Pr(sum<8) = 1-35/216 = 181/216 Hence Probability is 181/216 ~= 0.8379
_________________
Hades
|
|
|
|
|
|
Manager
Joined: 14 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 3
Kudos [?]:
18
[0], given: 1
|
eschn3am wrote: bmwhype2 wrote: Antmavel wrote: 1/2
min result : 3 (1+1+1)
max result : 18 (6+6+6)
number of outcomes : 18-3+1 = 16
We want outcome >10 and max is 18 so there are 8 possibilities over 16
8/16 = 1/2 whats the logic behind that equation? 3 dice: lowest number possible 1+1+1 =3, greatest number possible 6+6+6=18 18-3+1 (because inclusive) = 16 possible outcomes. 8 of which are greater than 10 but certain sums come up more frequently than others... ie you get 3 (1+1+1) 1/216 of the time but 4 (1+1+2,1+2+1,2+1+1) 3/216 = 1/72 of the time...
_________________
Hades
|
|
|
|
|
|
GMAT Instructor
Joined: 07 Jul 2003
Posts: 773
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 5
Kudos [?]:
9
[0], given: 0
|
KASSALMD wrote: There is no need for any calculations here. No matter what the numbers are, the probability will always be 1/2. The reason for that is that Joe can have only 2 outcomes- either outscore Mary or be outscored. Simple, isn't it! It would have been a different question if it was required to find out probability of Joe getting a particular score. This is incorrect. You are right that they are two outcomes "of interest", but they are NOT either outscore Mary or be outscored. They are outscore mary and NOT be outscored (i.e., can tie). And just because there are two outcomes of interest doesn't mean they have equal probability.
_________________
Best,
AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
|
|
|
|
|
|
Senior Manager
Joined: 23 Jun 2009
Posts: 368
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 4
Kudos [?]:
86
[0], given: 60
|
Hades is true. A perfect answer.
|
|
|
|
|
|
Intern
Joined: 11 Feb 2013
Posts: 22
Followers: 0
Kudos [?]:
1
[0], given: 4
|
Re: Mary and Joe throw three dice each. If Mary gets 10, what [#permalink]
22 Mar 2013, 07:23
not able to understand this ques and any of the solution mentioned above.. if anyone can explain me in some other way ...then please explain  thanks in advance
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10121
[0], given: 963
|
Re: Mary and Joe throw three dice each. If Mary gets 10, what [#permalink]
22 Mar 2013, 07:26
|
|
|
|
|
|
|
Re: Mary and Joe throw three dice each. If Mary gets 10, what
[#permalink]
22 Mar 2013, 07:26
|
|
|
|
|
|
|
|
|
|
|
close
