November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
CEO
Joined: 15 Aug 2003
Posts: 3382

Baseball's World Series matches 2 teams against each other
[#permalink]
Show Tags
Updated on: 10 May 2014, 04:25
Question Stats:
55% (01:17) correct 45% (01:56) wrong based on 163 sessions
HideShow timer Statistics
Baseball's World Series matches 2 teams against each other in a bestofseven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games? (A) 12.5% (B) 25% (C) 31.25% (D) 68.75% (E) 75% OPEN DISCUSSION OF THIS QUESTION IS HERE: baseballsworldseriesmatches2teamsagainsteachother3120.html
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Praetorian on 07 Jan 2004, 00:09.
Last edited by Bunuel on 10 May 2014, 04:25, edited 1 time in total.
Edited the question and added the OA.



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

Re: PS : World Series
[#permalink]
Show Tags
07 Jan 2004, 05:57
praetorian123 wrote: Baseball's World Series matches 2 teams against each other in a bestofseven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?
(A) 12.5% (B) 25% (C) 31.25% (D) 68.75% (E) 75%
please explain
Isn't this a previous Manhattan GMAT question of the week?



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

Probability that league is finished in 6 games = 1  P
where P = probability that league is finished in 7 games.
In order to go for seven games each team has to win 3 each in the first 6 games
Total combinations are 6! / ( 3! * 3! ) = 20
The last game has two combinations ( win or lose )
so total combinations = 20 * 2 = 40
Since each game has two possible values 7 games will have 2^7 = 128
P = 40/128
Probability that league is finished in 6 games = 140/128 = 88/128
= 68.75
Please post the correct answer.



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

anandnk wrote: Probability that league is finished in 6 games = 1  P where P = probability that league is finished in 7 games. In order to go for seven games each team has to win 3 each in the first 6 games Total combinations are 6! / ( 3! * 3! ) = 20 The last game has two combinations ( win or lose ) so total combinations = 20 * 2 = 40 Since each game has two possible values 7 games will have 2^7 = 128
P = 40/128
Probability that league is finished in 6 games = 140/128 = 88/128 = 68.75
Please post the correct answer.
That is the correct answer  i don't think you needed anyone to tell you that.



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

Hmm. I am not very confident is solving probability questions. I do solve permutation/combination problems well. I even dont know baseball or playing cards( unsual right  I dont attempt probs with deck of cards, I need to know about cards ). SO I definitely needed the answer.
Thanks



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

[#permalink]
Show Tags
Updated on: 07 Jan 2004, 09:06
anandnk wrote: Hmm. I am not very confident is solving probability questions. I do solve permutation/combination problems well. I even dont know baseball or playing cards( unsual right  I dont attempt probs with deck of cards, I need to know about cards ). SO I definitely needed the answer.
Thanks
Your explanation is very close to Manhattan GMAT's official answer  it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 20 ├Ч 2 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability that the World Series will last less than 7 games is 100%  31.25% = 68.75%.
The correct answer is D."
Originally posted by Titleist on 07 Jan 2004, 09:03.
Last edited by Titleist on 07 Jan 2004, 09:06, edited 1 time in total.



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

This is unbelievable. Truely I came up with it on my own. I did try combination of 4,5 and 6 games.



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

anandnk wrote: This is unbelievable. Truely I came up with it on my own. I did try combination of 4,5 and 6 games.
I believe you! No innuendos here. Just fascination.



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

I have a problem with this question let me know where I am wrong.
If number of games played is to be less than 7 then a team can win
either in first 4 games or 4 games in 5 or 4 games in 6
so desired combinations are
4C4 + 5C4+6C4 = 1+5+15 = 21
Total combinations = 7C4 = 35
so Proability that seven games are not played = 21/35 = 3/5 = 0.6
How is this possible ?



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

anandnk wrote: I have a problem with this question let me know where I am wrong.
If number of games played is to be less than 7 then a team can win either in first 4 games or 4 games in 5 or 4 games in 6 so desired combinations are 4C4 + 5C4+6C4 = 1+5+15 = 21
Total combinations = 7C4 = 35 so Proability that seven games are not played = 21/35 = 3/5 = 0.6 How is this possible ?
I don't know what it is you're exactly trying to show here. Although I have an idea  but in any case it's not making much sense to me.



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

I used reverse probability to get the correct answer. However the other method should also give me the same result right.
I would like you to tell me what is wrong with my recent aproach. I am getting 60% instead of 68.75%



Senior Manager
Joined: 28 Oct 2003
Posts: 492
Location: 55405

When you use, for example, 6c4, you ignore the possibility that some of those iterations are AAAABB, or the like in other words, you're counting a series where one team loses the first four games and somehow wins the rest.
Since after losing 4 games a team is eliminated, some of those scenarios are impossible.
On the other hand, I'm drunk right now, so I might have misunderstood you...



Director
Joined: 14 Oct 2003
Posts: 579
Location: On Vacation at My Crawford, Texas Ranch

stoolfi wrote: When you use, for example, 6c4, you ignore the possibility that some of those iterations are AAAABB, or the like in other words, you're counting a series where one team loses the first four games and somehow wins the rest.
Since after losing 4 games a team is eliminated, some of those scenarios are impossible.
On the other hand, I'm drunk right now, so I might have misunderstood you...
stoolfi  you kill me! i'm quite drunk myself. however, mr. anandank, i'm giving up 4 minutes of sleep just to show you the error in your method.
there are 4c4 ways of winning 4 out of 4 games. and the probability is 1/2^4 since you're playing 4 games.
secondly, 4 out of 5 games...5c4 right??? WRONG!!!
write them down
LWWWW
WLWWW
WWLWW
WWWLW
WWWWL exclude
so you have 4 secnarios (x2) multiply by 1/2^5
thus 2/(2^4)
Lastly you have 4 out of 6 games
Scenarios
LLWWWW
WLLWWW
WWLLWW
WWWLLW
LWLWWW
WLWLWW
WWLWLW
LWWLWW
WLWWLW
LWWWLW
so you have 10 scenarios x 2 = 20 scenarios multiplied by 1/2^6
thus you have 20/64+8/32+2/16=44/64=0.6875 or 68.75%
But why the heck would you ever want to do it this way?
I'm going to bed! It's freak'n close to 3 am?!



SVP
Joined: 30 Oct 2003
Posts: 1750
Location: NewJersey USA

Thanks a lot fellas It was helpfull I see my mistake now.



Retired Moderator
Joined: 17 Sep 2013
Posts: 344
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: Baseball's World Series matches 2 teams against each other
[#permalink]
Show Tags
09 May 2014, 23:37
Praetorian wrote: Baseball's World Series matches 2 teams against each other in a bestofseven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?
(A) 12.5% (B) 25% (C) 31.25% (D) 68.75% (E) 75%
please explain We are calculating the total number of outcome as 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7 But here we assuming that W W W W W W W is a possibility I don't think the series would continue after 4 wins and hence this is not an outcome at all.. Should we not calculate the total outcomes as : No of ways we can arrange WWWWLLL (Even this is not a possible case but this is what I can think of right now)
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Math Expert
Joined: 02 Sep 2009
Posts: 50613

Re: Baseball's World Series matches 2 teams against each other
[#permalink]
Show Tags
10 May 2014, 04:37
JusTLucK04 wrote: Praetorian wrote: Baseball's World Series matches 2 teams against each other in a bestofseven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?
(A) 12.5% (B) 25% (C) 31.25% (D) 68.75% (E) 75%
please explain We are calculating the total number of outcome as 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^7 But here we assuming that W W W W W W W is a possibility I don't think the series would continue after 4 wins and hence this is not an outcome at all.. Should we not calculate the total outcomes as : No of ways we can arrange WWWWLLL (Even this is not a possible case but this is what I can think of right now) We do want to include WWWWWWW case, when we do 1  P(seven games) approach. This case would be one of the cases attributed to WWWW. The probability of this case is (1/2)^4. If you continue this to 7 games you get: WWWW WWW > P=(1/2)^7 WWWW WWL > P=(1/2)^7 WWWW WLW > P=(1/2)^7 WWWW LWW > P=(1/2)^7 WWWW WLL > P=(1/2)^7 WWWW LWL > P=(1/2)^7 WWWW LLW > P=(1/2)^7 WWWW LLL > P=(1/2)^7 Sum = 8*(1/2)^7 = (1/2)^4. The same probability as we got for WWWW. So, 1  P(seven games) would still give the correct answer. Baseball's World Series matches 2 teams against each other in a bestofseven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games? (A) 12.5% (B) 25% (C) 31.25% (D) 68.75% (E) 75% Say the teams are A and B. In order the series to consist of seven games each team has to win 3 games in the first 6 games: {A, A, A, B, B, B}. The probability that A wins is 1/2 and the probability that B wins is also 1/2, so the probability of {A, A, A, B, B, B} is (1/2)^6*6!/(3!3!). Therefore the probability that the series will consist of fewer than 7 games is \(1  (\frac{1}{2})^6*\frac{6!}{3!3!} = 0.6875\). Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: baseballsworldseriesmatches2teamsagainsteachother3120.html
_________________
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? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 8777

Re: Baseball's World Series matches 2 teams against each other
[#permalink]
Show Tags
25 Oct 2018, 22:17
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




Re: Baseball's World Series matches 2 teams against each other &nbs
[#permalink]
25 Oct 2018, 22:17






