A team has a record of 12 wins and 13 losses for the season. : GMAT Problem Solving (PS)
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# A team has a record of 12 wins and 13 losses for the season.

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A team has a record of 12 wins and 13 losses for the season. [#permalink]

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01 Nov 2009, 03:16
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A team has a record of 12 wins and 13 losses for the season. Three games remain. If the probability of winning each remaining game is 1/2, and there are no draws, what is the probability that the team will finish the season with a winning record ?

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 5/8
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Dec 2013, 01:13, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Probability of team's winning [#permalink]

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01 Nov 2009, 03:25
must be 1/8 since there are three games left and each game's win probability is 1/2 for three games its 1/8 (A)
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01 Nov 2009, 03:44
kirankp wrote:
must be 1/8 since there are three games left and each game's win probability is 1/2 for three games its 1/8 (A)

hmm.. the answer is correct, but the derivation is not
hint: think of the possible scenarios with the 3 games
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Re: Probability of team's winning [#permalink]

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01 Nov 2009, 04:02
the only way the team can end with a winning record is if they win all 3 games.

winning 2 games or less can in no way make wins>losses (which is necessary for condition of winning record).

therefore the probability of ending with a winning record = probability of winning all 3 games = (1/2)*(1/2)*(1/2) = 1/8

Ans: A (1/8)
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Re: Probability of team's winning [#permalink]

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02 Nov 2009, 23:19
anyone else wants to give it a try before the OA?
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Re: Probability of team's winning [#permalink]

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03 Nov 2009, 06:37
IMO 1/8

As the team will win the series only by winnning three games(even if it wins 2 or 1 game it will lose)

What is the OA
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Re: Probability of team's winning [#permalink]

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07 Nov 2009, 07:53
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Oops forgot to post the OA for this one: $$A$$

All of you got it right, and there are so many ways to reach a probability solution.. here is the official approach given:
Total possible outcomes: WWW, WWL, WLW, LWW, LWL, LLW, WLL, LLL. Total 8.
Favorable outcomes: WWW. Total 1.

Probablity=1/8
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Re: Probability of team's winning [#permalink]

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07 Nov 2009, 09:05
just want to comment on gmattokyo solution: you forget to add the fact that we need 3 wins to get the wining seasons. lets say if they have 12 L and 12 W and 3 to go, all they need is 2 W and the prob is 1/4.
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Re: Probability of team's winning [#permalink]

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10 Dec 2013, 09:16
sriharimurthy wrote:
the only way the team can end with a winning record is if they win all 3 games.

winning 2 games or less can in no way make wins>losses (which is necessary for condition of winning record).

therefore the probability of ending with a winning record = probability of winning all 3 games = (1/2)*(1/2)*(1/2) = 1/8

Ans: A (1/8)

I too agree with this approach. They obviously need to win the three games.

Cheers!
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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11 Dec 2013, 03:55
The team will have a positive record only by winning all the three matches remained. So it's just 1/2^3 right?

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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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11 Dec 2013, 03:57
Downunder87 wrote:
The team will have a positive record only by winning all the three matches remained. So it's just 1/2^3 right?

Yes, that is correct.
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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11 Dec 2013, 04:43
All the 3 games need to be won in order to get a winning streak.
So, required probability = 1/2 * 1/2 * 1/2 = 1/8

So, the correct answer is A.
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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19 Feb 2014, 04:29
Well the question asks "winning record". If I'm not wrong, winning record would mean winning the last game. Now everyone here is speaking of winning more than 14 games out of a total of 28 or winning 3 consecutive games. However, the question stem never mentions that "winning record" means the team must fulfil either of the two conditions (Winning 3 games consecutively or winning >14 games). If a layman is to be asked, what a "finishing the season with a winning record" means, isn't the expected answer be "Winning the last game".
Can I be kindly guided by the experts regarding the ambiguity I'm facing (the ambiguity regardind the question).
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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19 Feb 2014, 08:51
sgangs wrote:
Well the question asks "winning record". If I'm not wrong, winning record would mean winning the last game. Now everyone here is speaking of winning more than 14 games out of a total of 28 or winning 3 consecutive games. However, the question stem never mentions that "winning record" means the team must fulfil either of the two conditions (Winning 3 games consecutively or winning >14 games). If a layman is to be asked, what a "finishing the season with a winning record" means, isn't the expected answer be "Winning the last game".
Can I be kindly guided by the experts regarding the ambiguity I'm facing (the ambiguity regardind the question).

The question implies that winning record is winning more games than loosing. Since the current score is 12:13, then the team must win all of its 3 remaining games in order to achieve that.

Hope it's clear.
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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19 Feb 2014, 15:17
Bunuel wrote:
sgangs wrote:
Well the question asks "winning record". If I'm not wrong, winning record would mean winning the last game. Now everyone here is speaking of winning more than 14 games out of a total of 28 or winning 3 consecutive games. However, the question stem never mentions that "winning record" means the team must fulfil either of the two conditions (Winning 3 games consecutively or winning >14 games). If a layman is to be asked, what a "finishing the season with a winning record" means, isn't the expected answer be "Winning the last game".
Can I be kindly guided by the experts regarding the ambiguity I'm facing (the ambiguity regardind the question).

The question implies that winning record is winning more games than loosing. Since the current score is 12:13, then the team must win all of its 3 remaining games in order to achieve that.

Hope it's clear.

Bunuel,
I have I doubt. How do we get to know whether its winning the last game or winning more games than losing the last one. I thought the GMAT was trying to lure us to 1/8 but since it asked for winning record (which I understood as winning the last game), it would be independent of the other two. Hence, the ans would be 1/2.
I do know that I'm wrong (I'm not questioning the OA, but I simply couldn't get the answer)
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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19 Feb 2014, 23:38
sgangs wrote:
Bunuel wrote:
sgangs wrote:
Well the question asks "winning record". If I'm not wrong, winning record would mean winning the last game. Now everyone here is speaking of winning more than 14 games out of a total of 28 or winning 3 consecutive games. However, the question stem never mentions that "winning record" means the team must fulfil either of the two conditions (Winning 3 games consecutively or winning >14 games). If a layman is to be asked, what a "finishing the season with a winning record" means, isn't the expected answer be "Winning the last game".
Can I be kindly guided by the experts regarding the ambiguity I'm facing (the ambiguity regardind the question).

The question implies that winning record is winning more games than loosing. Since the current score is 12:13, then the team must win all of its 3 remaining games in order to achieve that.

Hope it's clear.

Bunuel,
I have I doubt. How do we get to know whether its winning the last game or winning more games than losing the last one. I thought the GMAT was trying to lure us to 1/8 but since it asked for winning record (which I understood as winning the last game), it would be independent of the other two. Hence, the ans would be 1/2.
I do know that I'm wrong (I'm not questioning the OA, but I simply couldn't get the answer)

Finishing the season with a winning record, at least for me, naturally means winning more games than loosing...
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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24 Mar 2014, 07:08
I actually overlooked the fact that if they win only two, the third will automatically be a loss, which will increase the total losses. Sigh. Guess I have a looooong way to go...
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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02 Aug 2014, 03:56
Bunuel you are correct. Then shouldn't we be looking at keeping more wins than loses? Team as of now has 12 wins and 13 loses. So shouldn't we look for winning 2 games rather than all three so that we just maintain the winning streak. Thinking in these lines i opted for answer 3/8 that is LWW, WLW and WWL. Please let me know where i am going wrong. Thanks in advance.
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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02 Aug 2014, 09:09
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sri30kanth wrote:
Bunuel you are correct. Then shouldn't we be looking at keeping more wins than loses? Team as of now has 12 wins and 13 loses. So shouldn't we look for winning 2 games rather than all three so that we just maintain the winning streak. Thinking in these lines i opted for answer 3/8 that is LWW, WLW and WWL. Please let me know where i am going wrong. Thanks in advance.

The team must finish the whole season with a winning record, if it wins 2 and losses 1, then it finishes the season with 14 wins and 14 losses, which is NOT a winning record. Only winning all 3 games guarantees a winning record.

Hope it's clear.
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Re: A team has a record of 12 wins and 13 losses for the season. [#permalink]

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02 Aug 2014, 23:05
gmattokyo wrote:
A team has a record of 12 wins and 13 losses for the season. Three games remain. If the probability of winning each remaining game is 1/2, and there are no draws, what is the probability that the team will finish the season with a winning record ?

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 5/8

I got 1/8. Came up with the same solution as everyone else. Thanks for the question.
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Re: A team has a record of 12 wins and 13 losses for the season.   [#permalink] 02 Aug 2014, 23:05
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