#3 - For any given ticket in a 1000 ticket lottery, it is

[est15]

I got this one right but I was stuck for some time between (A) and (C). I paraphrased the flawed reasoning as "low chance doesn't mean it'll never happen." It seemed like both answers fit this reasoning. What made (A) a better choice than (C)? Did I frame the reasoning too broadly? I think one of my problems with parallel reasoning is I'm not sure how closely the right answer needs to fit with the original method of reasoning. Could you give some tips for that?

Thanks!

[Steve Stein]

Hi,

That's an interesting question. In that one, the author's argument can be broken down as follows:

It is reasonable to believe that any given ticket in a 1000 ticket lottery will lose
Therefore it is reasonable to believe that no ticket will win.

Correct answer choice (A) parallels this flawed reasoning nicely:

It is reasonable to believe that any given card drawn from a deck will not be an ace.
Therefore it is reasonable to believe that no card will be an ace.

Incorrect answer choice (C) presents a flaw that looks similar, but has subtle differences:

It is unreasonable to believe that 1000 coin flips will turn up heads,
Therefore it is reasonable to believe that this never happens.

Note some distinctions: both the stimulus and the correct answer choice base a conclusion about the reasonableness of one belief on the reasonableness of another belief.

Incorrect answer choice (C) concludes that a belief is reasonable based on the fact that another belief is unreasonable.

Both (A) and (C) present flawed reasoning, but (A) is the one that best parallels the stimulus.

I would also be suspicious of answer choices (B), (C), and (D) from the outset, because they all deal with 1000 events; this is a related topic but has nothing to do with paralleling the logic of the author's argument (not that such answers couldn't be right in other cases--I just try to beware of answers that have familiar features of questionable relevance).

I hope that's helpful--please let me know whether this is clear--thanks!

~Steve

[est15]

Hi Steve,

I remember from the Logical Reasoning Bible that for parallel reasoning, the presence of a negative term is not enough to eliminate the answer. Why is it then that we can eliminate (C) simply because it uses the word "unreasonable" rather than "reasonable"?

Thanks!

[Steve Stein]

Hi,

You're right; certainly, in many cases you cannot glean anything from the positivity or negativity of an answer choice--always being absent, for example, is logically equivalent to never being present.

In the question that you asked about, the difference between using a reasonable belief to prove something and using an unreasonable belief to prove something makes correct answer choice (A) the closer parallel, all else equal.

Another point worth noting is that both the stimulus and correct answer choice (A) deal with a single event--none of the tickets in a single lottery will win, none of the cards in a single deck will be an ace--while incorrect answer choice (C) draws the flawed conclusion that 1000 heads-up flips in a row never happens.

Thanks for your response--I hope that's helpful--please let me know whether this is clear--thanks!

~Steve