NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 02:27 It is currently 25 Apr 2024, 02:27
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

The Red Jackets and Blue Blazers are playing for the

User avatar
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
The Red Jackets and Blue Blazers are playing for the [#permalink] New post   09 Mar 2007, 08:04
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
The Red Jackets and Blue Blazers are playing for the championship. The first team to win a total of four matches is declared the winner and no more matches are played. If the two teams are equally likely to win any match and no match ends in a draw, what is the probability that at least six matches will be played?

(A) 3/8 (B) 7/16 (C) 1/2 (D) 9/16 (E) 5/8

*****



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 Problem Solving (PS) 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
BG
Senior Manager
Senior Manager
Joined: 13 Nov 2003
Posts: 357
Own Kudos [?]: 176 [0]
Given Kudos: 0
Location: BULGARIA
Concentration: INSURANCE, RISK MANAGEMENT
 Q49  V38
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   09 Mar 2007, 08:59
Hi,
The prob that each of the teams will win first 4 games is (1/2)^4 or 1/16
So the prob that the game will end in 4 games is (1/16)+(/16)1/8
The prob that the game will end in 5 games is 4/16 for team A and 4/16 for team B and the required prob is 4/16+4/16=1/2
The prob that the winner will be selected in 4 or 5 games is 1/8+1/2 or 5/8
The prob that 6 or more games will be played is 1-(5/8)=3/8

So 3/8 is my choice
User avatar
ricokevin
Manager
Manager
Joined: 11 Feb 2007
Posts: 193
Own Kudos [?]: 1012 [0]
Given Kudos: 0
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   11 Mar 2007, 04:10
Man, I was trying to solve this prob using combinatorics... :?
like in order for there to be at least six games played, a team has to at least have won 2 games, and expand from there...

BG's answer is pretty much straight forward I think. It seems correct. :-D

Guess I have a long way to go to get 51 in math :cry:
User avatar
SimaQ
Senior Manager
Senior Manager
Joined: 06 Feb 2006
Posts: 435
Own Kudos [?]: 498 [0]
Given Kudos: 0
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   11 Mar 2007, 04:20
BG wrote:
Hi,
The prob that each of the teams will win first 4 games is (1/2)^4 or 1/16
So the prob that the game will end in 4 games is (1/16)+(/16)1/8
The prob that the game will end in 5 games is 4/16 for team A and 4/16 for team B and the required prob is 4/16+4/16=1/2
The prob that the winner will be selected in 4 or 5 games is 1/8+1/2 or 5/8
The prob that 6 or more games will be played is 1-(5/8)=3/8

So 3/8 is my choice


How did you get 4/16 as the probability to end the series in 5 games?...
User avatar
ricokevin
Manager
Manager
Joined: 11 Feb 2007
Posts: 193
Own Kudos [?]: 1012 [0]
Given Kudos: 0
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   11 Mar 2007, 04:32
SimaQ wrote:
BG wrote:
Hi,
The prob that each of the teams will win first 4 games is (1/2)^4 or 1/16
So the prob that the game will end in 4 games is (1/16)+(/16)1/8
The prob that the game will end in 5 games is 4/16 for team A and 4/16 for team B and the required prob is 4/16+4/16=1/2
The prob that the winner will be selected in 4 or 5 games is 1/8+1/2 or 5/8
The prob that 6 or more games will be played is 1-(5/8)=3/8

So 3/8 is my choice


How did you get 4/16 as the probability to end the series in 5 games?...


To end the series in 5 games, the winning team has to have won 4 games and lost one. There are 4 ways of winning 4 games and losing one:
l w w w w
w l w w w
w w l w w
w w w l w

(not w w w w l cuz if the team won 4 straight games, it'd end there!)

and the prob of a team winning 4 games is (1/2)^4 = 1/16

Therefore, (1/16)x4 = 4/16
User avatar
mbagal1
Director
Director
Joined: 28 Dec 2005
Posts: 696
Own Kudos [?]: 107 [0]
Given Kudos: 0
 Q49  V45
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   11 Mar 2007, 05:52
I am going to give this a try, I get 9/16.

The probability asked is:

1 - (P(one team wins the first 4 games) + P(one team wins 4 games in the first 5 games)

= 1 - 2* (4C4 * (1/2)^4 + 5C4*(1/2)^4*(1/2) ) - multiplying by 2 since it can happen to either team.

= 1 - (2 /16+ 5/16) = 1-7/16 = 9/16.
User avatar
mbagal1
Director
Director
Joined: 28 Dec 2005
Posts: 696
Own Kudos [?]: 107 [0]
Given Kudos: 0
 Q49  V45
Send PM
Re: The Red Jackets and Blue Blazers are playing for the [#permalink] New post   11 Mar 2007, 06:03
Just saw ricokevin's response. Ok, so it looks like when I calculated the probability of winning 4 in 5 games, I have included again, the probability of winning 4 games straight.



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 Problem Solving (PS) 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: The Red Jackets and Blue Blazers are playing for the [#permalink]
11 Mar 2007, 06:03
Moderators:
Bunuel
Math Expert
92904 posts
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