A statistician reached the following conclusions about games between

Question

A statistician reached the following conclusions about games between university soccer teams: Overall, a team playing on its home field has a 45% chance of a win, a 25% chance of a loss, and a 30% chance of a draw (a tied outcome). In the games where one or more goals are scored, the team that scores the first goal has a 55% chance of scoring it in the game's first half and a 45% chance of scoring it later in the game. When that team is the home team (i.e., a team playing on its home field), there is a 40% chance that the other team will score no goals at all, and therefore a 60% chance that it will score one or more goals.
Select for X and for Y two different outcomes such that the information provided explicitly includes the statistician's estimates of the probability that if X occurs, so will Y. Make only two selections, one in each column.

Select for  X  and for  Y  two different outcomes such that the information provided explicitly includes the statistician's estimates of the probability that if X occurs, so will Y. Make only two selections, one in each column.

ID: 700225

KarishmaB · Accepted Answer

Frankly, the question makes me uncomfortable. To "include the statistician's estimates of the probability" I would expect something like "If A happens, B is more likely to happen" not "If A happens, so will B". This construct means that A is sufficient for B and it cannot reflect higher probability of B compared with 'not B'.
Of course since all options mention definite outcomes, I will assume that the "more than 50% probability" means "will happen" but I would do it only to guess the answer to this question and move on quickly. 
Since if "the home team scores the first goal," there is a 60% chance that the other team will score a goal too, I will select "The team opposing the home team scores at least one goal" and move on. 
I wouldn't yet like to call it a learning or a takeaway from this question. Hopefully an actual GMAT question wouldn't have this wording.

chetan2u · Answer

The probability scenarios are
 
  Team playing on Home ground: W-45%, L-25% and D-30% 
  Games where at least one goal scored: First goal in first half - 55%;  If home team scores first goal, 60% chances the other team will score at least one goal   
Let us look at the question and the options:
So, we are looking at X happening translating in more than 50% chances of Y happening. 
 If X, then more than 50% chances of Y happening.

Options: Let us take each as X, and see if some other option fits in as Y.

A. The home team scores at least two goals in the game.
We do not have a scenario where home team scores at least two goals resulting in some other option.

B. The home team scores the first goal.
Look at the point (2) in brown. If 'The home team scores the first goal.' is happening, then 60% probability that other team will score at least one goal. Option E gives us the exact words, so would fit in as Y.

C. A goal is scored in the first half of the game.
If ' A goal is scored in first half(55%), then Y can be 'the games where one or more goals are scored'. But that has to be true and we do not have any option fitting in as Y.

D. A goal is scored in the second half of the game.
Is it the first goal of the match or one of many scored? No situation in the para, so does not fit in as X.

E. The team opposing the home team scores at least one goal.
There is nothing connected to this option, so cannot fit in as X. However it is connected and dependent on another situation given in option B, and can fit in as Y.

X : The home team scores the first goal.
 Y : The team opposing the home team scores at least one goal.

Nullbyte · Answer

The question says "If x occurs so will y" doesn't this mean that Y has to occur 100% if X has occurred?

Posted from my mobile device

chetan2u · Answer

The question doesn't straighyway mention that. There are certain words used which point towards probabilities.

Select for X and for Y two different outcomes  such that the information provided explicitly includes the statistician's estimates of the probability  that if X occurs, so will Y. Make only two selections, one in each column.

Iwillget770 · Answer

Hi  chetan2u ,

Why does option 2 for X and 3 for Y does not fit ?

If X ie  The home team scores the first goal , then Y ie  A goal is scored in the first half of the game.

Here the probability of A goal is scored in the first half of the game is 55 % which is more than 50 %

Regards

chetan2u · Answer

Iwillget770 ,
In the games where one or more goals are scored, the team that scores the first goal has a 55% chance of scoring it in the game's first half. 
The above is based on stats of matches that were collected by the statistician. But we do not know the break down of home team and visitor team.

Say, Visitor team scores 6 times in first half in the 10 times it has scored first goal, while for home team it is 5 times in 10 goals they scored first. . 
Combined probability is 11 times in 20 matches, that is 55%, but the probability for home team is 50%.

It is somewhat similar to a student of a school scoring 75% on an average. We cannot extend it different parts, that is the girls will also average 75%.

Iwillget770 · Answer

Hi  chetan2u ,

I cannot understand the above logic. Sorry for asking you to explain again

Let me try to explain my logic
As per the Question:
 
Here   IT   refers to the  FIRTST GOAL 
ie
 Say Visitor team scores 10 times and Visitor Team scores the FIRST. Now as per the question there is a 55 % probability that the first goal will be in the first half. 
ie out of 10 goals, there is 55 % probability that the first goal will be scored in 1st half. Now , we are not concerned with rest of the 9 goals. The rest of the 9 goal can be scored in the 2nd half.

As per your explaination
 
According to me , the question is not saying that If 20 goals are scored in a match then 55%(6+5=11) of the goals will be scored in 1st half.

Accoring to my comprehension
The question explicity says that If  A Team  scores the  first goal , then the proability of scoring that  first goal  in  1st half  is 55 %.

Regards

chetan2u · Answer

Hi
 Iwillget770 , I dont think I was able to make my point clear. I am also talking of only times when the goal ahs been scored in first half.
Let me try it again...

Statistician:  In the games where one or more goals are scored, the team that scores the first goal has a 55% chance of scoring it in the game's first half. 
The above is based on stats of matches that were collected by the statistician. There has to be a basis for probability.

A team scoring first goal is 55% likely to score in first half. But we do not know the break down of home team and visitor team separately. The 55% probability is for Home team and visitor team combined.

But we can have different scenarios:
(I) 
Visitor team scores the first goal 10 times out of which 6 times the goal has been in first half.
However, home team scores the first goal 10 times again out of which exactly 5 times the goal was scored in first half.
Combined for both teams, out of 20(10+10) times the team scoring first goal scored the goal 11(6+5) times in first half. Thus, probability for a team is 11 times in 20 matches, that is 55%, but the probability for home team separately is 50%.

(II)
But if someone says that the probability is same for a home team and visitor team, then both will also have 55% separately.

It is somewhat similar to probability of a student to be from grade 10 is 15%, because grade 10 had 150 students and the school strength was 1000. 
But can we say probability of a girl student to be from grade 10 is 15%? No, it will depend on how many total girls are there in grade 10 and in school.
Here student = team and girl student = home team.

Elite097 · Answer

KarishmaB  if there’s a 60% of chance of them scoring a goal then how can it be a necessary condition since it’s not 100% necessary and there is a 40% that it won’t score any goal

If home team scores first goal, 60% chances the other team will score at least one goal. I’m really not clear on this question

Posted from my mobile device

manasp35 · Answer

Breakdown of question statement :

"probability that if X occurs, so will Y"

meaning what is the probability that if X occurs, Y will happen ?

statistician has the estimate of this probabilty and the information includes this estimate clearly.

saynchalk · Answer

I don't understand how we get to 60%, everything in this question seems convoluted

manasp35 · Answer

p(no goals) + P(one or more) = 100

40 + P = 100

saynchalk · Answer

Thanks! <img src="{SMILIES_PATH}/1f604.png" class="forumSmileyItem" width="20" height="20" alt=":D" title="Very Happy" />

Oppenheimer1945 · Answer

@ chetan2u 
Very Poorly framed question. Stats given are of no use that one learns probability from class 12 Maths. This ques doesn't even test the concept of mutually exclusive events, exhaustive events, Baye's theroem , continuous /graphical probability, Principle of Inclusion&Exclusion. They have just puked all numbers in this argument.

Looks like GMAC is intending to reduce the overall score of candidates by putting in such questions.

playthegame · Answer

At first I thought this was a conditional probability problem, then I looked at the options and I was not sure if that was the case.

I think if you spend a min or two extra you will figure out the answer, not very rational.

Gemmie · Answer

Home team wins : 45% 
  Home team loses : 25% 
  Home team draws : 30% 
  First goal in first half : 55% 
  First goal in second half : 45% 
  If the home team scores the first goal, the other team scores no goals : 40% 
  If the home team scores the first goal, the other team scores one or more goals : 60%

X: The home team scores the first goal  
 Y: The team opposing the home team scores at least one goal :

The provided information tells us explicitly that if the home team scores the first goal, the probability of the opposing team scoring no goals is 40%, and the probability of them scoring one or more goals is 60%. This matches the relationship we are looking for.

Vordhosbn · Answer

I agree with  KarishmaB  - when I read the stem saying 'outcome B will happen,' I was under the impression that there is a situation (i.e., outcome A) that will trigger outcome B 100% of the time, i.e., guaranteed outcome. But this is an actual GMAT question right? I.e., published by GMAC? Is there a way to report these? If these are GMAC published questions, what prevents them from giving students these subpar wordings on an actual test?

KarishmaB · Answer

You have the option of reporting content errors to GMAC on mba.com (left bottom of a practice question). If enough people raise concern about a particular question, they may re-evaluate it. You can report this one and see what they say. 
The quality control on actual questions will be far higher.

shvm_sin7 · Answer

No, the question states that if X occurs so  will  Y. But it is only a probability of 60% that the opposing home team scores at least one goal

A statistician reached the following conclusions about games between

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

X	Y
		The home team scores at least two goals in the game.
		The home team scores the first goal.
		A goal is scored in the first half of the game.
		A goal is scored in the second half of the game.
		The team opposing the home team scores at least one goal.

GMAT Two-part Analysis (TPA) Questions

A statistician reached the following conclusions about games between

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards