It is currently 20 Oct 2017, 20:26

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A and B decide to play a game based on probabilities. They

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 358

Kudos [?]: 453 [1], given: 50

Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Reviews Badge
A and B decide to play a game based on probabilities. They [#permalink]

Show Tags

New post 07 Aug 2012, 07:17
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (03:37) correct 50% (01:32) wrong based on 36 sessions

HideShow timer Statistics

A and B decide to play a game based on probabilities. They throw a fair dice alternately, whoever gets a 5 on his throw wins. What is the probability that A wins the game, if it is known that B starts the game?

A. 7/12
B. 5/12
C. 5/11
D. 7/11
E. 1/2
[Reveal] Spoiler: OA

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html


Last edited by Bunuel on 07 Aug 2012, 07:45, edited 1 time in total.
Edited the question.

Kudos [?]: 453 [1], given: 50

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129046 [1], given: 12187

Re: A & B decide to play a game based on probabilities [#permalink]

Show Tags

New post 07 Aug 2012, 07:44
1
This post received
KUDOS
Expert's post
SOURH7WK wrote:
A and B decide to play a game based on probabilities. They throw a fair dice alternately, whoever gets a 5 on his throw wins. What is the probability that A wins the game, if it is known that B starts the game?

A. 7/12
B. 5/12
C. 5/11
D. 7/11
E. 1/2


The probability that A wins the game after the first round is \(\frac{5}{6}*\frac{1}{6}\) (B must get anything but 5 and A must get 5);

The probability that A wins the game after the second round is \((\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{1}{6})\) (both must get anything but 5 in the first round and A must win in the second round);

The probability that A wins the game after the third round is \((\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{1}{6})\);

and so on...

The overall probability that A wins, will be the sum of the above probabilities: \(\frac{5}{6}*\frac{1}{6}+(\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{1}{6})+(\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{5}{6})*(\frac{5}{6}*\frac{1}{6})+...\)

Notice that we have the sum of the terms of geometric progression with the first term equal to \(\frac{5}{6}*\frac{1}{6}=\frac{5}{36}\) and the common ratio equal to \(\frac{5}{6}*\frac{5}{6}=\frac{25}{36}\).

Now, the sum of infinite geometric progression with common ratio \(|r|<1\), is \(sum=\frac{b}{1-r}\), where \(b\) is the first term.

So, the above sum equals to \(\frac{\frac{5}{36}}{1-\frac{25}{36}}=\frac{5}{11}\).

Answer: C.

P.S. Not a GMAT type of question.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129046 [1], given: 12187

Manager
Manager
avatar
Joined: 23 Jan 2011
Posts: 128

Kudos [?]: 119 [0], given: 13

Re: A and B decide to play a game based on probabilities. They [#permalink]

Show Tags

New post 08 Aug 2012, 09:58
wow that's complicated, I had it till the point where the probability of A winning in the 3rd round is:
(5/6 x 5/6) x (5/6 x 5/6) x (5/6 x 1/6), but beyond that you lost me on the Geom Progression.

Bunuel is it important to know GP inside out for the GMAT? I've done Arithmetic Progression of course..

Kudos [?]: 119 [0], given: 13

Intern
Intern
avatar
Joined: 03 May 2012
Posts: 1

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

Re: A and B decide to play a game based on probabilities. They [#permalink]

Show Tags

New post 08 Aug 2012, 10:06
Thanks for the solution

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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16637

Kudos [?]: 273 [0], given: 0

Premium Member
Re: A and B decide to play a game based on probabilities. They [#permalink]

Show Tags

New post 03 Oct 2017, 13:41
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

Kudos [?]: 273 [0], given: 0

Re: A and B decide to play a game based on probabilities. They   [#permalink] 03 Oct 2017, 13:41
Display posts from previous: Sort by

A and B decide to play a game based on probabilities. They

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.