Critical Reasoning

Tony: I play the Big Bucks lottery. Every week, five winning numbers are drawn, and all the players who have picked those numbers share the jackpot. It's best to play only after there have been a few weeks with no winners, because the jackpot increases each week that there is no winner.

Baggs: No, you're more likely to win the lottery when the jackpot is small, because that's when the fewest people are playing.

Which one of the following most accurately describes a mistake in the reasoning of one of the two players?

(A) Tony holds that the chances of winning are unaffected by the number of times a person plays.
(B) Baggs holds that the chances of Tony's winning are affected by the number of other people playing.
(C) Tony holds that the chances of anyone's winning are unaffected by the size of the jackpot.
(D) Baggs holds that the chances of Tony's winning in a given week are unaffected by whether anyone has won the week before.
(E) Tony holds that the chances of there being a winner go up if no one has won the lottery for quite a while.

Source: Veritas Prep

[spoiler]OA: B[/spoiler]

My Analysis:
(A) Tony never mentioned about number of times a person plays. This statement does not show mistake in Tony's reasoning.

(B) Baggs meant that the chances of tony's winning are affected by the number of other people playing. But this is not flawed reasoning. Of course chance (or probability) of one player's winning is affected by the number of participating players. If there are 100 people playing, chance (or probability) of anyone's winning is 1/100. If there are 1000 people playing, chance (or probability) of anyone's winning is 1/1000. If there are 20000 people playing, chance (or probability) of anyone's winning is 1/20000. Thus the statement does not show mistake in Bagg's reasoning.

(C) Tony never correlated the chances of anyone's winning with the size of the jackpot. This statement does not show mistake in Tony's reasoning.

(D) Baggs never mentioned that the chances of Tony's winning in a given week are unaffected by whether anyone has won the week before. This statement does not show mistake in Bagg's reasoning.

(E) Tony never mentioned that the chances of one's a winning go up if no one has won the lottery for quite a while. He just told that the jackpot increases each week that there is no winner. This statement does not show mistake in Tony's reasoning.

In my view, there is no correct answer. Requesting experts to comment on this.

magpie16 wrote:Tony: I play the Big Bucks lottery. Every week, five winning numbers are drawn, and all the players who have picked those numbers share the jackpot. It's best to play only after there have been a few weeks with no winners, because the jackpot increases each week that there is no winner.

Baggs: No, you're more likely to win the lottery when the jackpot is small, because that's when the fewest people are playing.

Which one of the following most accurately describes a mistake in the reasoning of one of the two players?

(A) Tony holds that the chances of winning are unaffected by the number of times a person plays.
(B) Baggs holds that the chances of Tony's winning are affected by the number of other people playing.
(C) Tony holds that the chances of anyone's winning are unaffected by the size of the jackpot.
(D) Baggs holds that the chances of Tony's winning in a given week are unaffected by whether anyone has won the week before.
(E) Tony holds that the chances of there being a winner go up if no one has won the lottery for quite a while.

Source: Veritas Prep

[spoiler]OA: B[/spoiler]

Great question. Took me some time to get to B. That too I got thru POE. Thanks ....keep posting more!

Magpie -

I can see why you would think that B is not correct. Normally, the odds of winning are impacted by the number of people participating. For example, if you are trying to be the person with the highest numbered card drawn from a deck and everyone draws a card at random your odds do in fact depend on the number of people who are playing. If there are 5 people you have odds of 1/5 if 10 people then 1/10.

However, in this case you are not trying to beat the other people, but you are trying to match the five numbers. This is why it does not matter how many people are playing. The way a Lotto works is they draw five numbers and if you match all five you win. You do not play against other people. Now of course if someone else also matches then you have to split the prize as you are "co-winners" but your odds of winning are not impacted.

It does say in the question " Every week, five winning numbers are drawn, and all the players who have picked those numbers share the jackpot." So you are only trying to match, not to beat the others.

That must have been frustrating. I can see how that would not seem correct.

Oops! A small trick knocked me hard!
Thank you, David, for the excellent explanation. I admit that I paid little attention to the part "all the players who have picked those numbers share the jackpot" and thus missed the point that the chance is considered here on picking the winning numbers (and not on beating other players)! Shame on me!

David@VeritasPrep wrote:Magpie -

I can see why you would think that B is not correct. Normally, the odds of winning are impacted by the number of people participating. For example, if you are trying to be the person with the highest numbered card drawn from a deck and everyone draws a card at random your odds do in fact depend on the number of people who are playing. If there are 5 people you have odds of 1/5 if 10 people then 1/10.

However, in this case you are not trying to beat the other people, but you are trying to match the five numbers. This is why it does not matter how many people are playing. The way a Lotto works is they draw five numbers and if you match all five you win. You do not play against other people. Now of course if someone else also matches then you have to split the prize as you are "co-winners" but your odds of winning are not impacted.

It does say in the question " Every week, five winning numbers are drawn, and all the players who have picked those numbers share the jackpot." So you are only trying to match, not to beat the others.

That must have been frustrating. I can see how that would not seem correct.

Okay, maybe not "shame on you" but there is a lesson to take from this - no outside knowledge and read carefully without making big assumptions.

The GMAT does try to play on your previous knowledge and get you to think in the wrong direction. Keep the questions coming! Making mistakes is the best way to learn!

Thank you, David. Definitely there is learning from every mistake. The frustrating thing is that in some cases GMAT needs our outside knowledge up to a certain level and in some cases GMAT expects us to behave as an "academic robot".

David,
A quick question.
In the first argument Tony never mentions anything about the relation between the number of people and winning chances. That is, Tony's simply says that he will play sometime after few weeks. So, he can win large amount.

Baggs argument is flawed because it explicitly assumes that winning chances decrease with the increase in number of people.

So, Isn't the reasoning of Baggs mistaken because he assumes that winning chances decrease with the increase in number of people.

Please correct me if I am not thinking it correctly.

That is exactly correct. He assumes that the more people playing the lower the chance of winning. You are not wrong in your thinking and that is why the answer is B. The question stem just asks you for a flaw in ONE of the two speaker's reasoning. So it could have been Tony's error or Baggs's error.