Tony: I play the Big Bucks lottery. Every week, five winning numbers

Question

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.

aditya8062 · Accepted Answer

B it is :   Baggs holds that the chances of Tony’s winning are affected by the number of other people playing.

why others are wrong:

A) Tony holds that the chances of winning are unaffected by the number of times a person plays.---->Tony is NOT talking about the chances. he is talking about much like  "Ghar baitho jeeto"  jackpot of KBC (kaun banegaa crorepati)
(B) Baggs holds that the chances of Tony’s winning are affected by the number of other people playing.----->correct !!
(C) Tony holds that the chances of anyone’s winning are unaffected by the size of the jackpot.-----> tony is NOT talking about chances of winning  
(D) Baggs holds that the chances of Tony’s winning in a given week are unaffected by whether anyone has won the week before ---->Baggs is talking about chances of winning when less people are playing 
(E) Tony holds that the chances of there being a winner go up if no one has won the lottery for quite a a while. ----> tony is not talking about chances

aditya8062 · Answer

it is a flaw because the chances of winning a lotto is not dependent on the number of people playing the lotto (as described in the premise). the probability is dependent on number of numbers that are there in the lot . ALSO read the following premise:  all the players who have picked those numbers share the jackpot ---->implies that there can be multiple winner .you might get a small share of (say $5) BUT you still be a winner !!

Udai · Answer

reasoning for C to be 
if Size of jackpot goes up then number of participants will go up (as per bags) if the number of participants go up then the chances of winning will decrease ... thus it should be considered as a flaw .. shouldn't it ?

TehMoUsE · Answer

"Every week, five winning numbers are drawn,and all the players who have picked those numbers share the jackpot." Your chance of winning is 1/10000 regardless of how many participants in the lottery. There will probably be more people picking the winning numbers (since a higher prize pool attract more players), but the chance if picking the winning numbers is still the same (1/10000). 0.0001 chance of winning ----> Size of jackpot goes up ----> Still 0.0001 chance of winning --------------- "Baggs: No, you’re more likely to win the lottery when the jackpot is small,because that’s when the fewest people are playing." Baggs does exactly this mistake of believing that the number of people participating affect the chance of winning (B) Baggs holds that the chances of Tony’s winning are affected by the number of other people playing. Hence, B is correct. Hope this helps! Sidenote: Your thinking was the same as Baggs in this story :-D

karant · Answer

Hello,

In order to conclude that winning a loto is independent on the number of people playing the lotto requires one assumption that the set of numbers does not increase when there are more people.

For e.g. - for first week there are 100 participants, so numbers 1 to 100 are distributed among the participants and out of those 100, five numbers are lucky numbers.

Now, suppose in second week, the number of participants is increased to 1000, so now numbers 1 to 1000 are distributed among the larger participants. Hence, probability of winning is decreased.

In my opinion, if the stem had mentioned the range of numbers, may be 1 to 100 or 1 to 1000, distributed in Big Bucks lottery system, then it would have been more sound.

Thanks

KarishmaB · Answer

That is not how the lottery is played. How do lottery tickets work? Players can either choose their own six numbers (five regular and one Powerball) or have the computer terminals randomly pick numbers for them. If every number on your ticket matches the winning numbers in the order they are drawn, you win the jackpot prize. ... Each ticket costs the player $1 This is what a lotto ticket would look like: 160115171656-lottery-winners-revealed-on-tv-lawyer-reaction-randy-zelin-nr-00000130-exlarge-169.jpg People can pick any 5 numbers of their choice. Hence, 10 people could pick the same 5 random numbers. If those numbers are called, they share the jackpot. Hence, it is possible that no one wins if no one picks the winning combination. The question assumes a certain knowledge about how the lottery works because it is something which is very well known in US. For international students, it could be tricky and an official question would give all details of how it works to ensure a level playing field.

kornn · Answer

Dear VeritasKarishma IanStewart , I know that choice D. is incorrect because Baggs does not say so. However, I think it is interesting to apply Quant skill in attacking this choice from Probability's perspective as well. (D) Baggs holds that the chances of Tony’s winning in a given week are unaffected by whether anyone has won the week before . Is the highlighted portion mathematically valid? I think winning a lottery is an independent event . What occurred the week before has NO effects on the chances of winning this week. Since it is mathematically valid, choice D. CANNOT be a flaw (or "a mistake in the reasoning") in the argument EVEN IF Baggs says so! Please help

KarishmaB · Answer

(D) Baggs holds that the chances of Tony’s winning in a given week are unaffected by whether anyone has won the week before. Option (D) is not accurate. We will worry whether the reasoning is flawed or not later. First thing is that Bahhs does not hold this. He says, "You’re more likely to win the lottery when the jackpot is small, because that’s when the fewest people are playing." This means that Baggs thinks that if someone won the jackpot the week before, the jackpot will be small and so few people will play which increases the probability of a win. So as per him, winning in a week is AFFECTED by whether anyone has won the week before. So this is not Braggs reasoning at all. Whether it is flawed or not is irrelevant then. As for mathematically, is this reasoning valid? Yes it is. The chances of Tony’s winning in a given week are UNAFFECTED by whether anyone has won the week before. - this is true The chances of winning are NOT affected by how many people are playing. I have discussed this in my comment above: https://gmatclub.com/forum/tony-i-play- ... l#p2292228

IanStewart · Answer

Yes, if a question asks for a "logical flaw" in an argument, the right answer will indeed need to state a logical flaw. Answer D neither states a flaw nor describes something Baggs said, so D is wrong for two reasons.

Answer D is mathematically correct -- your lottery numbers aren't more likely to win this week if they lost last week -- though people often disbelieve that in real life. Some people think that if "29" hasn't come up recently on a roulette wheel, it's "due" to come soon. People thinking that way are succumbing to what is known as "the gambler's fallacy". If the roulette wheel is fair, each spin is independent, and the chance of getting "29" is the same every spin.

But if "29" hasn't come up in a while, then if there's any chance the wheel is unfair, that would make it likely the wheel is biased not to land on 29 as often as it should. So if 29 hasn't come up in a while, you'd do better by betting on some number other than 29 if the wheel might be unfair (i.e. it would be a mistake to bet that 29 is "coming soon", as people who believe in the gambler's fallacy would).

But if you know the results are purely random, as is presumably true of most lotteries (and in almost all GMAT probability questions), then the result last time has no bearing on the result next time. Each event is purely independent of each other event.

finisher009 · Answer

The core of the issue lies in understanding how a lottery works. The probability of a specific set of numbers being drawn is fixed and is not influenced by how many people are playing.
• If you pick the numbers 1-2-3-4-5, your chance of winning is the same whether one person is playing or one million people are playing.
• The number of players only affects the probability of having to share the jackpot if you win. With fewer players, you are less likely to have to share.

Baggs makes a mistake by confusing the probability of winning with the probability of winning without sharing. He incorrectly states that you are “more likely to win” when fewer people play.
Evaluating the Options

• (A) Tony holds that the chances of winning are unaffected by the number of times a person plays. Tony doesn’t discuss this. His focus is on when to play, not how often.

• (B) Baggs holds that the chances of Tony’s winning are affected by the number of other people playing. 
This is the correct answer. Baggs explicitly says, “you’re more likely to win... because that’s when the fewest people are playing.” This is a direct statement claiming the number of players affects the odds of winning, which is a logical flaw.

• (C) Tony holds that the chances of anyone’s winning are unaffected by the size of the jackpot. 
Tony doesn’t comment on the chances of winning at all; he comments on when it’s “best” to play, which relates to the size of the prize.

• (D) Baggs holds that the chances of Tony’s winning in a given week are unaffected by whether anyone has won the week before.
This describes an independent event, which is a correct assumption in a lottery. Therefore, it is not a mistake in reasoning.

• (E) Tony holds that the chances of there being a winner go up if no one has won the lottery for quite a while.
This is the Gambler’s Fallacy. Tony doesn’t make this mistake; he correctly states that the jackpot goes up, not the chances of winning.

The correct choice is (B) because it accurately identifies the flawed reasoning in Baggs’s argument.

Tony: I play the Big Bucks lottery. Every week, five winning numbers

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Tony: I play the Big Bucks lottery. Every week, five winning numbers

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