Event Independence on the LSAT

AnthonyScalia

Hello again! First of all, I wanted to express my general appreciation for everyone in the 7Sage community! You guys are essentially total strangers, yet almost always go the extra mile to help and support each other. I'm very impressed, and I feel privileged to be among you.

As for my question, I wanted to inquire about how the LSAT treats independent events in relation to likelihood. The content that spiked my curiosity came from Mike Kim's LSAT trainer rather than an official LSAT passage, so if this issue is not relevant to the LSAT, I'd love to know that too. The trainer has an exercise where one has to use proper knowledge of LSAT meanings for "some" and "most" to determine whether or not a statement in valid.

One of these statements is that "Everyone who orders a sundae gets offered a free extra cherry, and most people say yes to the extra cherry. Some people who order the banana split get offered a free extra cherry, and less than half of these people say yes. Therefore, people who order a sundae are more likely to say yes to a free cherry than are people who order a banana split."

Using the LSAT definitions of the qualifier words, Sundae buyers have a 1.0 chance of being offered, and more than half of them say yes. Banana Split Buyers have a 0 to 1.0 chance of being offered, and fewer than half accept. The conclusion then maintains that /people/ who order a Sundae are more likely to say yes to a free cherry than their heathen Banana-Split ordering counterparts; the book later designates this as a valid statement.

This situation immediately reminded me of a common mistake people make in evaluating confidence intervals in statistics. A 95% confidence interval, for example, does not mean that any given member of a population has a 95% chance of meeting a certain criteria. Rather, they already have have either a 0% chance or a 100% chance of meeting that criteria; their status (or in this context, selection,) is fixed and independent of any outside conditions. There is no roll of the dice. The interval merely gives us insight into the qualities of the group as a whole. In a way, this principle is reminiscent of the piece = puzzle LR flaw.

In the cited problem, we have data regarding the proportions of entities who made a decision being equated with the likelihood of those rigid entities from making one decision or the other, which isn't true.

So what does this situation mean for the LSAT? My guess is that this kind of situation would never arise on an LSAT, but if it does, I hope to find out whether my aforementioned thought process is correct, (thus invalidating the ice cream statement,) or if the LSAT does indeed require us to treat a population proportion and the "decision likelihoods" of its individual members as congruent values.

Thanks!

inactive

bumping this to the top

dcdcdcdcdc

I think I understand the distinction you are making here (how likely is person X to say yes vs. what is the likelihood of a person in a group having a certain property). In my reading of what you have excerpted from the Trainer, I think the context doesn't allow us an inference on how likely an individual person is to say yes, but instead the question is going after the proportion that said yes from each of the sundae and banana split groups. In this case, the key part of the statements is that most sundae persons said yes, whereas less than half of an already reduced number (by the some statement) of banana split persons said yes (i.e., most said no). That is the inference to be made here that a majority of one group said yes while a majority of the other said no.

I'm mapping it out as follows:

Sundae --> Offered cherry
Sundae -m-> say yes

Banana split <-s->offered cherry <-s-> say yes