riskiness vs likelihood

[aznriceboi17]

If in a LSAT passage I see the statement:
'Person A is at higher risk of contracting heart disease than Person B.'

is that equivalent to:
'Person A is more likely to contract heart disease than Person B.'

or are there in fact differences?

I've seen both words used frequently and I don't think I've ever noticed a distinction being made in any of the questions, but I wanted to double check.

[christine.defenbaugh]

Very interesting question!

The short answer is that these statements are fundamentally the same. If Joe is at higher risk of being hit by an asteroid than Mary, then Joe is more likely to be hit by an asteroid than Mary.

However, in order for them to be truly the same, you do have to make absolutely certain the rest of the language matches up. For instance, these two statements are not equivalent:

Joe faces higher risks from heart disease than Mary.
Joe is more likely to contract heart disease than Mary.

Notice the language differences. In the first sentence, what exactly are these risks? Does Joe face more risk simply of getting heart disease? Or is the author trying to say he's more at risk for death or serious issue as a result of heart disease? It's not perfectly clear, so we should be skeptical of their equivalence.

But if the rest of the language truly is identical, then the phrases "higher risk" and "more likely" would have the same essential meaning.

Please let me know if that answers your question!

[aznriceboi17]

That does help -- the example you gave is something that I was worried about and clarifies things for me. Thanks!

[ivank]

Perhaps I have missed similar discussions elsewhere on the forum, so please direct me to the place where my questions are relevant or with similar discussions...

I am a little confused with most likely, more likely, less likely, not likely/unlikely, not at all likely, etc. What does it mean in terms of numerical values?

How about the statement "it is not unlikely"... can it be properly transformed into "it is likely"? Does it necessarily mean more than 50% probability/chance?

Do you advise to think of it terms of numbers when reading statements involving the likelihood on LSAT? That's reading and imagining the numbers, then calculating some probabilities, dependent/independent events...


Part2: Is there a good way to translate those(see below)? I understand that LSAT makes it complicated, but I thought may be it is me who makes it more difficult than it really is.

Examples:
1) Most voters are unlikely to be persuaded by Astorga's campaign promises to vote for her in the mayoral election - My thinking: 6/10 voters would be persuaded less than 5/10x by A's campaign promises...Is this kind of thinking appropriate, or too complex, or too simple? Please share your thoughts.

2) It is likely, for example, that Isaac Newton's psychological
problems were due to mercury poisoning; traces of
mercury were found in his hair. - please share your thinking on this...

3) A birth is more likely to be difficult when the mother is over
the age of 40 than when she is younger. - please share your translation of this...

All of the above examples are taken form MLSAT LR Guide 3rd Ed.

Thanks in advance.
Ivan

[christine.defenbaugh]

Really interesting question, ivanushk!

The first thing I'll say is that a lot of the time, the numerical precision is not really required to have a sense of what the argument is saying. Only a few arguments really require that we break down the numbers.

Occasionally, however, breaking out the numbers during your review process can help you wrap your head around a particular concept or phrasing. That can in turn help to give you an intuitive grasp of the same issue when it arises on a new question.

Here's a quick list of very basic definitions:

Greater than 50% chance

probably
likely
more likely than not
fairly likely
extremely likely
very high probably
most likely*

Less than 50% chance

probably not
unlikely
fairly unlikely
extremely unlikely
very low probably
likely not
most likely not

"not unlikely" = the possibility is 50% or greater. The is NOT the same as 'likely'.

"not likely" = the possibility is 50% or less. This is NOT the same thing as 'unlikely' or 'likely not'.

"more likely" = used to compare two possibilities. X might have a 10% change, while Y has a 9% chance.

"the most likely"*= the outcome referred to is more likely than any other specific outcome.

*Note the difference between "the most likely" and "most likely". Imagine I'm deciding whether to get a red, green, or blue car. I tell you that "the most likely color will be red". That means it is more likely I'll get red than blue, and it's more likely that I'll get red than green. It does NOT tell you that I'm "most likely" to get red.

The chances could be:
red = 40%
blue = 30%
green = 30%

Out of the three, red is more likely than any one other color. But it's not more than 50%, so we wouldn't say "the car will mostly likely be red".

Your specific example are interesting. Some of them are definitely you making it too complicated! But that's good news, because it is relatively easy to fix! For the sake of future readers, where these examples are from in the real LSATs:

Preptest 22, S2, Q6, Answer choice (C)
You're working way to hard to understand the fine details of an incorrect answer. The important thing is that this answer goes to how voters are actually going to vote, while the argument is about whether Astorga is telling voters the truth. What most voters will do, how likely they are to be persuaded, etc - all muck you don't want to mire yourself in!

Preptest 28, S3, Q16
The bit you're quoting is merely part of the background information about mercury. The numerical likelihood here is not relevant to the argument core about Beethoven.

Preptest 16, S3, Q24
Here, the likelihood matters for the meat of the question!

"A birth is more likely to be difficult when the mother is over
the age of 40 than when she is younger."

We've got two groups of mothers, and each group has a likelihood of having a difficult birth. That likelihood is higher for the over-40 moms than for the younger moms. Maybe the younger moms have a 10% difficult birth chance, while the over-40 moms have a 12% difficult birth chance. Or maybe it's 10% vs 80%. We don't know.

The key in that question is that we don't know how big the two groups are, just their relatively chances. If the group of over-40 moms is tiny, then even with higher likelihood of difficult births, it's still not going to be a big number.



I know this was a lot of information, so please let me know if any of it is still a bit confusing, and I'll do my best to clear it up!

[ivank]

First of all, thanks a lot for clearing a few things out, and of course, for such a wonderful effort! Most of them are clear now. Just one question: you mentioned

"not unlikely" = the possibility is 50% or greater. The is NOT the same as 'likely'.

From above, it seems that "not unlikely" can be treated the same as "likely", numerically; but they are still not the same in meaning (please correct if I misunderstood). Would be I correct in reading it as "pretty likely" or "fairly likely"? Either way, what would be, in your mind, a synonym for "not unlikely"? Perhaps a couple of makeshift sentences if you can to help me clear this out? If I do that myself I confuse myself even more...

Thanks in advance.

P.S I am kind of thinking..."not unlikely" is the negation of "unlikely", which is not necessarily polar opposite "likely", is this what you meant? ...LSAT twists the mind out of me

[christine.defenbaugh]

Thank you for the follow-up question, ivank!

I think you're starting to circle in on the answer to your question in your last paragraph - that the negation of 'unlikely' is not precisely the same thing as likely. Your original statement that they could be treated the same way numerically is not actually correct. Let me put the relevant definitions side-by-side, and I want you to give yourself a moment to see if you can spot the difference.

"unlikely" = less than 50% chance
"not unlikely" = 50% or greater chance
"likely" = greater than 50% chance.

Did you find it?

The difference is whether 50% is included in the definition! Getting heads on a coin flip is not unlikely. It's not likely either. It's 50/50!

Now, I will point out that the vast majority of the time, that subtle distinction will not matter for the question - so don't go applying this by force all over! But it's not a bad thing to get a firm grip on as part of your foundational understanding of probability language.

Does that clear it up?