NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 15:21 It is currently 24 Apr 2024, 15:21
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In a certain game, a one-inch square piece is placed in the

User avatar
arjtryarjtry
Current Student
Joined: 11 May 2008
Posts: 377
Own Kudos [?]: 1029 [0]
Given Kudos: 0
Concentration: General
 Q50  V34
Send PM
In a certain game, a one-inch square piece is placed in the [#permalink] New post   02 Aug 2008, 02:24
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
durgesh79
Manager
Manager
Joined: 27 May 2008
Posts: 231
Own Kudos [?]: 622 [0]
Given Kudos: 0
Send PM
Re: In a certain game, a one-inch square piece is placed in the [#permalink] New post   02 Aug 2008, 12:18
arjtryarjtry wrote:
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL


imagine xy plane with intial position of piece at (0,0)
it can move 8 places in right or up direction

distance will be 4sqrt(2) when the final location is (4,4)

Final location - number of ways to reach there
(0,8) ---------- 8C0 = 1
(1,7) -----------8C1 = 8
(2,6)------------8C2 = 28
(3,5)------------8C3 = 56
(4,4)------------8C4 = 70 ....... (frankly i stopped here and marked option C .. but i dont recommend it)
(5,3)----same as (3,5) = 56
(6,2)------- = 28
(7,1)-------- = 8
(8,0)--------- = 1

probablity = 70/sum = 70/256.... answer
User avatar
durgesh79
Manager
Manager
Joined: 27 May 2008
Posts: 231
Own Kudos [?]: 622 [0]
Given Kudos: 0
Send PM
Re: In a certain game, a one-inch square piece is placed in the [#permalink] New post   05 Aug 2008, 02:09
arjtryarjtry : OA pls
User avatar
nmohindru
Manager
Manager
Joined: 06 Apr 2008
Posts: 158
Own Kudos [?]: 487 [0]
Given Kudos: 1
Send PM
Re: In a certain game, a one-inch square piece is placed in the [#permalink] New post   05 Aug 2008, 04:53
arjtryarjtry wrote:
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL


This will happen when number of up moves = Number of right moves = 4
User avatar
bhushangiri
Manager
Manager
Joined: 15 Jul 2008
Posts: 72
Own Kudos [?]: 395 [0]
Given Kudos: 0
Send PM
Re: In a certain game, a one-inch square piece is placed in the [#permalink] New post   05 Aug 2008, 05:26
durgesh79 wrote:
arjtryarjtry : OA pls


Don D,

I concur with your answer.. used gyan imparted by u in ur recent solution on 3,2 football match.. arrange n items where x are of type 1 and y are of type 2. n!/ x!y! :)

for (0,8) arrange 8 steps where 8 are of 1 type and 0 of another = 8!/8! = 1. (8,0) is also 1. total 2
for (1,7) and (7,1) arrange 8 steps where 7 are of 1 type and 1 of another. 8!/(7! 1!)= 8. 16 total.

similarly for 2,6 and 6,2 8!/(6! 2!) = 28. 56 total

for 3,5 and 5,3 8!/3!5! = 56. total 112

4,4 8!/4!4! = 70.

grand total = 70+112+56+16+2 = 256

favorable case = 70

prob = 70/256
User avatar
durgesh79
Manager
Manager
Joined: 27 May 2008
Posts: 231
Own Kudos [?]: 622 [0]
Given Kudos: 0
Send PM
Re: In a certain game, a one-inch square piece is placed in the [#permalink] New post   05 Aug 2008, 06:29
there is another way to calculate total number of chances ...
expand binomial expression (1+1)^8 = 2^8 = 256



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: In a certain game, a one-inch square piece is placed in the [#permalink]
05 Aug 2008, 06:29
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions