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 Adam Tyson
PowerScore Staff
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#84088
Here's where I think you went wrong, blade:
the conclusion can be paraphrased as: the Mars explorers would survive the trip
That's not a good paraphrase of the conclusion, because the actual conclusion is about probability, not certainty. It's not that the explorers would survive; it's that the risk of them dying is lower than some people think. The evidence about the backup at every stage means each individual stage (whether that is seen as a time element or a task element doesn't matter) has low risk, and the author concludes that the cumulative risk is therefore relatively low. My analogy about the long car trip isn't about the wear and tear on the tires, although that certainly would be a factor. It was about how risks build up. The longer you tempt fate, the more you run the risk of coming out on the losing end of that bet!

I'll borrow your marbles in a box example: if there are 100 marbles in the box, and only five of them are black, the odds of my selecting a black one when I reach in blindly are low. But what if I reach in, take one out, put it back, take another, put it back, take another, etc.? Don't the odds of my picking a black one begin to add up, such that you would expect that eventually I will pick one? That cumulative, growing risk is what the author here failed to consider. Low risk at any one stage does not mean low risk over the course of the entire trip.
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 rragepack
  • Posts: 14
  • Joined: Jan 22, 2021
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#87590
BethRibet wrote: Tue Sep 03, 2013 7:03 pm Hi,

Thanks for your question. Imagine that there are 40 stages involved in the long and complicated journey, and at each stage there's a 2% chance of a fatal catastrophe. Though the 2% chance at "any given stage", is minor, there are 40 instances where that small chance might come into play. That is, the chance of a catastrophe, though small at any given stage, is actually high overall. The whole journey is different from "any given stage", and that corresponds to answer choice A -- the whole is not identical to the parts, and we don't treat their characteristics as interchangeable.

Hope this helps!
Beth
Hi! I actually got this answer right because I thought 'A' was the best choice, but I disagree with the 2% argument and think that the question is not a very good example of the flaw of error of composition. If there is only a 2% chance of disaster at every stage of the trip, wouldn't the trip still be overall pretty safe because it's not like there is an 80% chance of disaster if there are 40 stages of a trip with 2% chance of failure on a trip. I believe that this goes the same for this question. It would be great if you could clarify things up for me! Thank you.
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 rragepack
  • Posts: 14
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#87591
rragepack wrote: Fri Jun 04, 2021 12:14 am
BethRibet wrote: Tue Sep 03, 2013 7:03 pm Hi,

Thanks for your question. Imagine that there are 40 stages involved in the long and complicated journey, and at each stage there's a 2% chance of a fatal catastrophe. Though the 2% chance at "any given stage", is minor, there are 40 instances where that small chance might come into play. That is, the chance of a catastrophe, though small at any given stage, is actually high overall. The whole journey is different from "any given stage", and that corresponds to answer choice A -- the whole is not identical to the parts, and we don't treat their characteristics as interchangeable.

Hope this helps!
Beth
Hi! I actually got this answer right because I thought 'A' was the best choice, but I disagree with the 2% argument and think that the question is not a very good example of the flaw of error of composition. If there is only a 2% chance of disaster at every stage of the trip, wouldn't the trip still be overall pretty safe because it's not like there is an 80% chance of disaster if there are 40 stages of a trip with 2% chance of failure on a trip. I believe that this goes the same for this question. It would be great if you could clarify things up for me! Thank you.
I think I understand now! Thanks!

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