A statistician reached the following conclusions about games between

­The probability scenarios are

1. Team playing on Home ground: W-45%, L-25% and D-30%
2. 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.


Guys, I also struggled with this question for quite a while. But I feel that students in this discussion are thinking about it wrongly. This is not a stats or a quant question.

It is truly just a verbal/RC style question, where you have to identify/recognise whether or not the STATISTICIAN'S ESTIMATE of the probabilities of a certain event to take place is provided in the above paragraph/the information provided to you.

Look closely at the other options. The information provided DOES NOT contain the probability estimates of those events, as given by the statistician. Take any other X,Y combination, and you will see that the information provided DOES NOT give us the statistician's estimate of the probabilities of that event (in that order) happening.

It's not a stats question saying "if X happens, then what WILL happen with 100% probability". It is just saying, "do we know the stats dude's estimate of the probability of this happening". And the inference "If X happens then what is the probability of Y happening by more than 50%" to me seems blatantly wrong. GMAC isn't a fool - and that is definitely a poor inference in my opinion.

Guys, I also struggled with this question for quite a while too. But I feel that students in this discussion are thinking about it wrongly. This is not a stats or a quant question.

It is truly just a verbal/RC style question, where you have to identify/recognise whether or not the STATISTICIAN'S ESTIMATE of the probabilities of a certain event to take place is provided in the above paragraph/the information provided to you.

Look closely at the other options. The information provided DOES NOT contain the probability estimates of those events, as given by the statistician. Take any other X,Y combination, and you will see that the information provided DOES NOT give us the statistician's estimate of the probabilities of that event (in that order) happening.

It's not a stats question saying "if X happens, then what WILL happen with 100% probability". It is just saying, "do we know the stats dude's estimate of the probability of this happening". And the inference "If X happens then what is the probability of Y happening by more than 50%" to me seems blatantly wrong. GMAC isn't a fool - and that is definitely a poor inference in my opinion.

­

All Data Insight question: TPA [ Official Guide DI Review 2023-24]

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.­

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.

In games where one or more

Here how do you decide that 'A goal is scored in the first half(55%) is X and 'the games where one or more goals are scored' is Y and not the other way round. Having a tough time establishing which is the bigger set here.

The statement "the probability that if X occurs, so will Y" refers to the likelihood of Y happening given that X has already occurred. In other words, it asks: "If X happens, how likely is it that Y will also happen?", i.e. conditional probability - p(Y|X)