The “Roll the Dice” Flaw

“Find the flaw” LSAT questions are both common and difficult. There are a lot of fallacies, and some of them are quite subtle.  The answer choices use “LSAT jargon” to describe each fallacy, not textbook Latin. That means you have to know the fallacy and the special LSAT terminology for it to answer the question with speed and confidence.

I recently ran across a “find the flaw” question that totally stumped me. I guessed one answer (with no confidence) on a timed test, then came back to blind review and picked another answer–still without any certainty. Both my choices turned out to be wrong, so I looked up the answer and promised to write a blog post about it. (I recommend this same procedure to students who want a 99th percentile score–you haven’t really mastered a question until you either know you got it right  or you write an essay about why you got it wrong.)

The question I had trouble with was PrepTest 65, Secton 4, #26. I won’t violate copyright by printing it here, so here’s a new problem with the same features. (If you own “10 Actual, Official LSAT PrepTests Volume V” you can find the actual question on page 143.

Nikola Tesla Magnet School accepts only the brightest students in our metropolitan region, so it boasts the best science club in the entire Tri-State Area. The best science club is most likely to win the annual robotics competition, so the Nikola Tesla Magnet School will almost certainly bring home the trophy this year.

I read this stimulus and immediately zeroed in on the difference between the best individual students and the best overall team. That’s such a common fallacy that it has a Latin name (“modo hoc“), although it’s not clear whether it applies in this case. But I never got that far because that wasn’t one of my answer choices. Here’s what was offered on the LSAT:

(A) presumes, without presenting relevant evidence, that an entity can be distinguished as the best only on the basis of competition.

(B) predicts the success of an entity on the basis of features that are not relevant to the quality of that entity.

(C) predicts the outcome of a competition merely on the basis of a comparison between the parties in that competition.

(D) presumes, without providing warrant, that if an entity is the best among its competitors, then each individual part of that entity must also be the best.

(E) concludes that because an event is the most likely of a set of possible events, that event is more likely to occur than not.

I was trying so hard to find a composition fallacy (that’s modo hoc for you Latin lovers) that I really wanted D to be correct, but it just wouldn’t work. I wound up picking C, then switched to A. B never appealed to me, and I never really understood what E was all about.

That was a mistake.

E is all about rolling dice. If I roll a pair of dice, seven is the most likely outcome. There are six out of thirty-six chances that I will roll a seven, making it more likely than any other roll (there’s a 1/36 chance of rolling two or twelve, a 2/36 chance of rolling three or eleven, etc., etc.). But just because seven is the single most likely roll, it’s not more likely to occur than not. I only roll a seven one out of six times. I’d have to roll it every other time (plus some) for it to be “more likely to occur than not.”

Most likely, but not more likely than not

That was my error. A science club may be “more likely” to win than any other club in the city, but that doesn’t mean it will “probably” win.

I’ve searched the Internet for the Latin name of this fallacy, and haven’t found it yet. You Latin buffs may refer to it as “alea jacta est.” The rest of us can just call it the “roll of the dice fallacy.”

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