BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Probability, 3 dice simultaneously

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 120
Joined: Thu Sep 02, 2010 8:56 am
Location: India
Thanked: 7 times
GMAT Score:730
by euro » Wed Sep 29, 2010 7:18 am
(Q) What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216

The official answer is [spoiler](a) [/spoiler]

Can somebody explain?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members
Location: London
Thanked: 70 times

by kmittal82 » Wed Sep 29, 2010 8:09 am
Wow, tough one...

Lets look at it case by case

#1) To get 8

8 = :

1+1+6
2+2+4
3+3+2
1+2+5
1+3+4


Since order won't matter, any combination of those 3 numbers will give you a sum of 8. Each combination can further have 6 arrangements


#2) to get 14
14 = :
6+6+2
6+5+3
6+4+4
5+5+4

Since order won't matter, any combination of those 3 numbers will give you a sum of 14. Each combination can further have 6 arrangements

Total outcomes on a roll = 6x6x6 = 216

Fav cases for getting 8 = 5x6/216 = 30/216
Fav cases for getting 14 = 4x6/216 = 24/216

Total probability = 54/216

Unfortunately though, its in neither of the answers, so I know Ive gone wrong somewhere... but where? :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members
Thanked: 29 times

by diebeatsthegmat » Wed Sep 29, 2010 9:30 am
euro wrote:(Q) What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216

The official answer is [spoiler](a) [/spoiler]

Can somebody explain?
for sum of 8 we will have
116 ( 161,611) thus there is 3 combination*2 =6 ( we have to multiply with 2 because the 3 dice are all different)
152 ,125, 215,251,512,521 thus there are 6 combination
the same with 143 we have 6 combination
total=18 ways thus probability=18/6*6*6
for sume of 14, we do the same above
266 , 635,464 and also have 18 ways
the probability is 18/6*6*6
total probability is 18/216+18/216=36/216=1/6
hope it helps
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Wed Sep 29, 2010 9:56 am
kmittal82 wrote:Wow, tough one...

Lets look at it case by case

#1) To get 8

8 = :

1+1+6
2+2+4
3+3+2
1+2+5
1+3+4


Since order won't matter, any combination of those 3 numbers will give you a sum of 8. Each combination can further have 6 arrangements
The bolded statement is your error.

For three different digits, such as 1+3+4, there are indeed 6 different arrangements. However, for the cases that have only 2 distinct digits, there are only 3 different arrangements.

So:

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

Total - 21 arrangements

Similarly for 14:

6/6/2 - 3 arrangements
6/4/4 - 3 arrangements
5/5/4 - 3 arrangements
6/5/3 - 6 arrangements

Total - 15 arrangements

Total possibilities is 6^3 = 216

Prob = # of desired outcomes / total # of possibilities

Prob = (21 + 15)/216 = 36/216 = 1/6
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members
Location: London
Thanked: 70 times

by kmittal82 » Wed Sep 29, 2010 11:30 am
Thanks for the explanation everyone :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members
Thanked: 29 times

by diebeatsthegmat » Wed Sep 29, 2010 4:59 pm
Stuart Kovinsky wrote:
kmittal82 wrote:Wow, tough one...

Lets look at it case by case

#1) To get 8

8 = :

1+1+6
2+2+4
3+3+2
1+2+5
1+3+4


Since order won't matter, any combination of those 3 numbers will give you a sum of 8. Each combination can further have 6 arrangements
thanks for the detail expanation but i thought the dices are different , of course it have the same numbers but its from different dice

The bolded statement is your error.

For three different digits, such as 1+3+4, there are indeed 6 different arrangements. However, for the cases that have only 2 distinct digits, there are only 3 different arrangements.

So:

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

Total - 21 arrangements

Similarly for 14:

6/6/2 - 3 arrangements
6/4/4 - 3 arrangements
5/5/4 - 3 arrangements
6/5/3 - 6 arrangements

Total - 15 arrangements

Total possibilities is 6^3 = 216

Prob = # of desired outcomes / total # of possibilities

Prob = (21 + 15)/216 = 36/216 = 1/6
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1