Q21 - Sandy: I play the Bigbucks lottery

[GRAMMOHAN.BUSINESS]

Why not answer choice E (Sandy holds that the chances of there being a winner....) is correct?

[bbirdwell]

Hello R,

Let me try to explain. On this problem, we must try to identify a flaw in one of the speakers' arguments, so me must analyze each argument and try to predict possible mistakes, or gaps in the reasoning.

Sandy says "it's best" to play the lotto only after there have been a few weeks without a winner because the money pot increases.

Alex disagrees, saying that one is more likely to win when the pot is small because fewer players are playing.

We can see that Alex makes the biggest mistake in logic here. When playing a lottery game based on choosing numbers that are to be drawn, your chances remain the same no matter how many other people are playing.

For example, let's pretend that you and I are playing a game where each of us selects one number between 1 and 10, and then the numbers 1-10 are thrown into a hat and one is drawn out. Your chances of winning are 1 out of 10. If we ask everyone in Boston to play the game, your chances of winning are still 1 out of 10. The number of people playing does not affect the probability of your guessing the winning number.

Thus, answer choice (B) is correct.

Answer choice (E) is incorrect because Sandy does not actually do what (E) suggests that she does. We know from the argument that Sandy believes it is BEST to play the lottery when no one has one it in quite awhile. She does not say, as (E) suggests, that the chances of there being a winner increase.

Hope that helps!

[hoffman36]

I just want to check my reasoning for why answer choice (D) is wrong:

Alex does not commit this flaw in his reasoning because his reply is constrained to the probability that Sandy will win during one drawing (at the end of the week). He doesn't discuss anything about previous weeks, and since they are irrelevant to the probability that Sandy will win anyways his lack of discussion about them isn't a flaw.

Is this correct?

Thanks!

[zhanga]

Actually D is incorrect because it states the opposite of what Alex is doing. Alex assumes that Sandy's chances of winning in a given week is affected by if anyone won the previous week since Alex says that your chances of winning increases if the pot is small and if the pot is small, then people haven't won in a while which implies if someone has won in the previous week, Alex probably believes your chances of winning will go down.

[WaltGrace1983]

Just to add, (A), (C), and (E) are all wrong because Sandy simply never talks about the "chances" of winning. We know that Sandy believes it is "BEST" to play when the pot is big. Why? Because that means more money! She doesn't really talk about the chances of anything.