Last visit was: 21 May 2024, 18:38 It is currently 21 May 2024, 18:38
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [14]
Given Kudos: 81918
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [2]
Given Kudos: 81918
Send PM
avatar
Intern
Intern
Joined: 02 Nov 2015
Posts: 14
Own Kudos [?]: 10 [2]
Given Kudos: 9
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 31 Mar 2016
Posts: 324
Own Kudos [?]: 196 [0]
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
Send PM
Re: M14-29 [#permalink]
I think this is a high-quality question and I agree with explanation.
Manager
Manager
Joined: 17 Sep 2014
Posts: 140
Own Kudos [?]: 53 [17]
Given Kudos: 6
Location: India
Concentration: Operations, Strategy
GMAT 1: 710 Q49 V38
GPA: 3.65
WE:Engineering (Manufacturing)
Send PM
Re: M14-29 [#permalink]
11
Kudos
6
Bookmarks
Yash26 wrote:
Hi,

I could not understand why we have only two arrangements? I understand that there are only two Ls and occurring first can happen in two ways but what is conceptually wrong in considering these three options -LWWLW, LLWWW & LWLWW? In all previous options loser is scoring first.

Please explain.

Regards
Yash



You can take it this way:
LLWWW can be arranged in 5!/(3!*2!), which is 10
Fixing the first goal to be scored by L, we get 4 slots remaining with LWWW, which can be arranged by 4!/3! leading to 4.

So, probability is 4/10 or 2/5.
:)
Manager
Manager
Joined: 13 Nov 2014
Posts: 92
Own Kudos [?]: 113 [0]
Given Kudos: 28
GMAT 1: 740 Q50 V40
Send PM
Re: M14-29 [#permalink]
Bunuel wrote:
Official Solution:

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? (Assume that all scoring scenarios have the same probabiliy)

A. \(\frac{1}{4}\)
B. \(\frac{3}{10}\)
C. \(\frac{2}{5}\)
D. \(\frac{5}{12}\)
E. \(\frac{1}{2}\)


Consider empty slots for 5 goals: *****. Say \(W\) is a goal scored by the winner and \(L\) is a goal scored by the loser. We need the probability of when \(L\) comes first while distributing these goals (5 letters \(LLWWW\)) into 5 slots.

Since there are 2 \(L\)'s out of total 5 letters, then \(P=\frac{Favorable}{Total}=\frac{2}{5}\).


Answer: C



Wow! Lesson learned. I was so set on using combinations to solve this that I completely missed the obvious and easy approach. Took me 3 mins to ensure that my probability was correct when I should have setup the answer the way you did and be done within 30 seconds.
Manager
Manager
Joined: 04 May 2014
Status:One Last Shot !!!
Posts: 196
Own Kudos [?]: 608 [3]
Given Kudos: 141
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
Send PM
Re: M14-29 [#permalink]
2
Kudos
1
Bookmarks
Bunuel wrote:
If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? (Assume that all scoring scenarios have the same probabiliy)

A. \(\frac{1}{4}\)
B. \(\frac{3}{10}\)
C. \(\frac{2}{5}\)
D. \(\frac{5}{12}\)
E. \(\frac{1}{2}\)


Total goals = 5
Winner goals = 3
Loser goals = 2

P (Loser hit the first goal) = P (Winner did not hit the first goal) = 1 - P (Winner hit the first goal)
=> 1- 3/5
=> 2/5
C
Intern
Intern
Joined: 23 Nov 2016
Posts: 44
Own Kudos [?]: 67 [0]
Given Kudos: 21
Location: United States (MN)
GMAT 1: 760 Q50 V42
GPA: 3.51
Send PM
Re: M14-29 [#permalink]
Bunuel wrote:
Official Solution:

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? (Assume that all scoring scenarios have the same probabiliy)

A. \(\frac{1}{4}\)
B. \(\frac{3}{10}\)
C. \(\frac{2}{5}\)
D. \(\frac{5}{12}\)
E. \(\frac{1}{2}\)


Consider empty slots for 5 goals: *****. Say \(W\) is a goal scored by the winner and \(L\) is a goal scored by the loser. We need the probability of when \(L\) comes first while distributing these goals (5 letters \(LLWWW\)) into 5 slots.

Since there are 2 \(L\)'s out of total 5 letters, then \(P=\frac{Favorable}{Total}=\frac{2}{5}\).


Answer: C


Is the reason why this is not 1/2 because the potential outcomes have already been dictated by the score? In other words, if the question stem had not provided the score of the game and the question was "what is the probability that Team A scores first?", then that probability would be 1/2?

However, because you are given the final score, there are 10 possible ways the game occurred:

LLWWW
LWLWW
LWWLW
LWWWL
WWWLL
WWLWL
WWLWL
WWLLW
WLWWL
WLLWW
WLWLW

The first four outcomes are the only ways the team could have not gotten the first goal out of the ten outcomes. P = 4/10 = 2/5

Correct?

P.S. - Can someone please express this in a combinatoric approach? I understand that there are 5c2 ways to arrange LLWWW, but how do we get the numerator to be 4? I believe it's (2c1)*2, since order of "which" L doesn't matter, but can someone please confirm?
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [0]
Given Kudos: 81918
Send PM
Re: M14-29 [#permalink]
Expert Reply
brooklyndude wrote:
Bunuel wrote:
Official Solution:

If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? (Assume that all scoring scenarios have the same probabiliy)

A. \(\frac{1}{4}\)
B. \(\frac{3}{10}\)
C. \(\frac{2}{5}\)
D. \(\frac{5}{12}\)
E. \(\frac{1}{2}\)


Consider empty slots for 5 goals: *****. Say \(W\) is a goal scored by the winner and \(L\) is a goal scored by the loser. We need the probability of when \(L\) comes first while distributing these goals (5 letters \(LLWWW\)) into 5 slots.

Since there are 2 \(L\)'s out of total 5 letters, then \(P=\frac{Favorable}{Total}=\frac{2}{5}\).


Answer: C


Is the reason why this is not 1/2 because the potential outcomes have already been dictated by the score? In other words, if the question stem had not provided the score of the game and the question was "what is the probability that Team A scores first?", then that probability would be 1/2?

However, because you are given the final score, there are 10 possible ways the game occurred:

LLWWW
LWLWW
LWWLW
LWWWL
WWWLL
WWLWL
WWLWL
WWLLW
WLWWL
WLLWW
WLWLW

The first four outcomes are the only ways the team could have not gotten the first goal out of the ten outcomes. P = 4/10 = 2/5

Correct?

P.S. - Can someone please express this in a combinatoric approach? I understand that there are 5c2 ways to arrange LLWWW, but how do we get the numerator to be 4? I believe it's (2c1)*2, since order of "which" L doesn't matter, but can someone please confirm?


Yes, that's correct.
User avatar
Intern
Intern
Joined: 03 Jan 2022
Posts: 5
Own Kudos [?]: 0 [0]
Given Kudos: 2
Send PM
Re: M14-29 [#permalink]
Although I got the question correctly, something that is still kind of a doubt is that, if we are asked the probability of the loosing team scoring first, and before the first goal is scored, wont the probability be 1/2 at the time of scoring the goal ? so idk if that makes sense but that was something that came to my mind while solving the problem but that seemed too far fetched and complicated so i choose the analog way of thinking about the question and went with 2/5
Founder
Founder
Joined: 04 Dec 2002
Posts: 37464
Own Kudos [?]: 73307 [0]
Given Kudos: 19002
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3
Send PM
Re: M14-29 [#permalink]
Expert Reply
vatsalcby wrote:
Although I got the question correctly, something that is still kind of a doubt is that, if we are asked the probability of the loosing team scoring first, and before the first goal is scored, wont the probability be 1/2 at the time of scoring the goal ? so idk if that makes sense but that was something that came to my mind while solving the problem but that seemed too far fetched and complicated so i choose the analog way of thinking about the question and went with 2/5



That's a good point. I like your thinking - at that point the probability of scoring is really 50/50 if the events are indeed independent but I think we don't know that both teams are equal in capability and this is not necessarily like flipping a coin that has a 50/50 chance. Any betting place will not give you a 50/50 chances for 2 teams ... I don't have an answer :lol:
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [1]
Given Kudos: 81918
Send PM
Re: M14-29 [#permalink]
1
Kudos
Expert Reply
bb wrote:
vatsalcby wrote:
Although I got the question correctly, something that is still kind of a doubt is that, if we are asked the probability of the loosing team scoring first, and before the first goal is scored, wont the probability be 1/2 at the time of scoring the goal ? so idk if that makes sense but that was something that came to my mind while solving the problem but that seemed too far fetched and complicated so i choose the analog way of thinking about the question and went with 2/5



That's a good point. I like your thinking - at that point the probability of scoring is really 50/50 if the events are indeed independent but I think we don't know that both teams are equal in capability and this is not necessarily like flipping a coin that has a 50/50 chance. Any betting place will not give you a 50/50 chances for 2 teams ... I don't have an answer :lol:


The original question asks for the probability that the losing team scored the first goal in a match that ended 3:2. While it may be tempting to think that the probability is 50% since there are only two possibilities for the first goal, this line of thinking is not correct. The actual score of the match determines the probability of each team scoring a goal, and therefore the probability that the losing team scored the first goal.

Consider the scenario where the match ends with a score of 5:0. Would you still say that the probability of the losing team scoring first is 50% in this scenario? In this case, the probability that the losing team scored the first goal is 0%, not 50%. This is because the actual score of the match eliminates the possibility of the losing team scoring any goals. Similarly, in the original scenario where the match ends 3:2, the actual score of the match determines the probability of each team scoring a goal, and thus the probability that the losing team scored the first goal is not simply 50%.
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [0]
Given Kudos: 81918
Send PM
Re: M14-29 [#permalink]
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33142
Own Kudos [?]: 829 [0]
Given Kudos: 0
Send PM
Re: M14-29 [#permalink]
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 Club Bot
Re: M14-29 [#permalink]
Moderator:
Math Expert
93373 posts