December 2010 LSAT Section 3 Question 8

A leading critic of space exploration contends that it would be wrong, given current technology, to send a group of e...

Ryn on January 23, 2022

Unlikelihood accumulating?

I have a hard time seeing this part to whole flaw. I’m a little confused here you all say that the risk adds up but we only know the likely hood of risk being unlikely so would the unlikely hood add up thereby strengthening the conclusion? We don’t know the likely hood of risk so how can we say that likelihood accumulates?

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Naryan-Shukle on January 24, 2022

Hey @Ryn,

I think this question touches on a very unintuitive and difficult concept to grasp, which is the idea of probability in running series.

If I flip 99 coins and they all land heads, what are the chances that I flip a 100th coin and it also lands heads? Most would say it's highly unlikely, but my coin still has two sides, and the chances are the same it's always been—50/50.

This is known as the gambler's fallacy, and it's the entire reason casinos make money: because it's unintuitive, and people think their luck will change, when math says differently.

Now, this is where concepts can get muddled. Just because my chance of flipping heads stays 50/50, that does NOT mean that I have 50/50 chances of hitting heads 100 times in a row. The "series" is very unlikely.

THIS is the part-whole flaw that our author makes. Chances don't "add up." Unlikelihood can't "stack." There's a low chance of failure in each discrete stage of the journey, but the SERIES of steps together, all occurring without one failure, is far less likely.

Think of it this way. If you get into a 100mph head-on car crash, what are the chances that you will damage your left cochlear hammer bone? Well that's crazy specific, so the chances I break EXACTLY that bone are low. Well, what about the 7th stabilizer bone in your hand? Again, very unlikely. It's just so random. I could do this over and over for every bone in the body. BUT, does this mean I have a low chance of breaking a bone in a 100mph head-on collision? Of course not! I'm extremely likely to break at least one bone. If you can understand why this example is flawed, you can understand the flaw in this question.

This is a tough subject in probability, so feel free to ask any questions if you're still unsure. Hope this helps!