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

It is currently 27 Aug 2015, 13:26
GMAT Club Tests

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

What is the probability of getting a sum of 8 or 14 when

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 07 Nov 2004
Posts: 690
Followers: 5

Kudos [?]: 35 [0], given: 0

What is the probability of getting a sum of 8 or 14 when [#permalink] New post 26 Nov 2004, 06:31
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (03:54) correct 69% (02:47) wrong based on 204 sessions
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
[Reveal] Spoiler: OA
4 KUDOS received
Intern
Intern
avatar
Joined: 16 Nov 2004
Posts: 26
Followers: 0

Kudos [?]: 6 [4] , given: 0

Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 26 Nov 2004, 06:51
4
This post received
KUDOS
2
This post was
BOOKMARKED
Quote:
"Gayathri"
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

Is there a shorter way to do this than listing each possibility?


I am confident that there is a better way, but I looked at the first few possibilities

throw a 3 - 1 way
throw a 4 - 3 ways
throw a 5 - 6 ways
throw a 6 - 10 ways

and recognized these as triangular numbers (the series could also be identified as add 2, add 3, add 4 ...).

from there it was easy to calculate that there are 21 ways to hit an 8 and 15 ways to hit a 14. (Problems with fair dice and coins produce symmetrical probability distributions, so one can count down from 1 way to throw an 18)

[more than 2 minutes - less than 3 minutes]
1 KUDOS received
Manager
Manager
User avatar
Joined: 31 Aug 2004
Posts: 166
Location: Vancouver, BC, Canada
Followers: 1

Kudos [?]: 5 [1] , given: 0

Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 26 Nov 2004, 22:03
1
This post received
KUDOS
Richie Weasel wrote:
Quote:
"Gayathri"
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

Is there a shorter way to do this than listing each possibility?


I am confident that there is a better way, but I looked at the first few possibilities

throw a 3 - 1 way
throw a 4 - 3 ways
throw a 5 - 6 ways
throw a 6 - 10 ways

and recognized these as triangular numbers (the series could also be identified as add 2, add 3, add 4 ...).

from there it was easy to calculate that there are 21 ways to hit an 8 and 15 ways to hit a 14. (Problems with fair dice and coins produce symmetrical probability distributions, so one can count down from 1 way to throw an 18)

[more than 2 minutes - less than 3 minutes]


Wow, Richie, this is a fast and easy way to solve it! I will take a note of this method!

:good
Manager
Manager
avatar
Joined: 30 Jul 2004
Posts: 101
Followers: 1

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

Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 27 Nov 2004, 22:06
Is there any other to solve this question ?

Can you elaborate the answer pls. ?
Director
Director
User avatar
Joined: 07 Nov 2004
Posts: 690
Followers: 5

Kudos [?]: 35 [0], given: 0

Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 28 Nov 2004, 05:05
1
This post was
BOOKMARKED
gmat+obsessed wrote:
Is there any other to solve this question ?


The other way would be to list out each option.
The options for a sum of 8: (6,1,1) has 3 options ie (6,1,1), (1,6,1), (1,1,6); (5,2,1) has 6 options, (4,3,1) has 6 options, (4,2,2) has 3 options, (3,3,2) has 3 options. We have 21 options to get 8.

The options for a sum of 14: (6,4,4) has 3 options, (6,5,3) has 6 options, (6,6,2) has 3 options, (5,5,4) has 3 options. We have 15 options to get 14.

Total: 21+15= 36/216 = 1/6.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6075
Followers: 339

Kudos [?]: 68 [0], given: 0

Premium Member
Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 12 Sep 2014, 05:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Senior Manager
Senior Manager
User avatar
Joined: 23 Jan 2013
Posts: 371
Schools: Cambridge'16
Followers: 2

Kudos [?]: 33 [0], given: 33

CAT Tests
Re: What is the probability of getting a sum of 8 or 14 when [#permalink] New post 22 Oct 2014, 04:17
I missed some options for 8 as a sum. Idea is that options containing three different number have 3!=6 possible events, options containing 2 identical and 1 other have 3!/2!*1!=3 possible events. By multiplying and summing we get the answer
1 KUDOS received
Intern
Intern
avatar
Joined: 15 Nov 2012
Posts: 2
Followers: 0

Kudos [?]: 2 [1] , given: 1

What is the probability of getting a sum of 8 or 14 when [#permalink] New post 17 Nov 2014, 13:03
1
This post received
KUDOS
Here's another way:
You start by listing out each possible triplet for every number on the dice for each of the two numbers we need (notice that for each triplet the probability is \(\frac{1}{6^3}\)):
8:
1:
[1,1,6]
[1,2,5]
[1,3,4]
[1,4,3]
[1,5,2]
[1,6,1]

2:
[2,1,5]
[2,2,4]
[2,3,3]
[2,4,2]
[2,5,1]

…and so on...

Soon thereafter, you realize that, for each number of the dice, there is one triplet less that adds up to 8, than the previous number (i.e. 1-triplets: 6, 2-triplets: 5, 3-triplets: 4, and so on…). Given that \(\frac{1}{6^3}\) is a common factor to all triplets, we get that: \(\frac{1}{6^3}*(6+5+4+3+2+1)\) or \(\frac{1}{6^3}*(21)\).

Then we do a similar process for 14:

1:
(No possible combination adds up to 14)

2:
[2,6,6]

3:
[3,5,6]
[3,6,5]

…and so on…

So you'll notice that a similar thing happens in this case: from 2 on, for each number of the dice, there is one triplet more that adds up to 14, than the previous number (i.e. 2-triplet: 1, 3-triplets: 2, 4-triplets: 3, and so on…). Again, given that \(\frac{1}{6^3}\) is a common factor to all triplets, we get that: \(\frac{1}{6^3}*(1+2+3+4+5)\) or \(\frac{1}{6^3}*(15)\).

Given that we need the probability of getting a sum of 8 OR 14, we add up both of these cases:
\(\frac{1}{6^3}*(21)+\frac{1}{6^3}*(15)\)

We factor out \(\frac{1}{6^3}\), and find that:
\(\frac{1}{6^3}*(36)\), and by recognizing that \(36 = 6^2\), we cross it out with \(6^3\) to find that the probability of getting a sum of 8 or 14 when rolling three fair dice is \(\frac{1}{6}\).

Answer A.
What is the probability of getting a sum of 8 or 14 when   [#permalink] 17 Nov 2014, 13:03
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If 6x=8y=14z, then what is a possible sum of positive integers x, y, a Bunuel 3 19 Jan 2015, 04:22
5 Experts publish their posts in the topic If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th Bunuel 3 05 Nov 2014, 07:16
Experts publish their posts in the topic What is the probability that you will get a sum of 8 when Amateur 2 18 Nov 2012, 15:07
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
19 Experts publish their posts in the topic What is the probability of getting a sum of 12 when rolling anhlukas 8 16 Aug 2006, 11:22
Display posts from previous: Sort by

What is the probability of getting a sum of 8 or 14 when

  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®.