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Accident and Incident Analysis:
Re: [ClimbClimb] Climbing gym disaster:
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jt512
Apr 27, 2010, 1:54 AM
Views: 10184
Registered: Apr 12, 2001
Posts: 21904
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ClimbClimb wrote: jt512 wrote: Well, in my humble opinion, you did not "make a minor approximation." You made a major mistake, leading to mathematically impossible results. As I stated above, your approach can lead to "probabilities" exceeding 1, which are nonsensical. If you want to "do the full math for me," please do, although I think I actually did it for you in my previous post. The funny thing is that we agree on the key point -- it is good to grab the rope. I was trying to avoid paragraphs of unnecessary nerdiness. The full math in this case would analyze the approximation, etc. Briefly, the point you're missing is that the probability of belayer failing are actually small quantities. My approximation was to say that (1-ab) is close to 1. That's true when "b" is a very small quantity, say 0.01 or 0.001. And, as you observed, it is not true if the probability of belayer failing is large, like 0.62 (or 62%). The full math would also include a parameter for repeated falls, etc. I am quite comfortable with this approximation being minor not because the *formula* is correct (it's not, that's why I mentioned I was making an approximation), but b.c. the result is correct for the likely set of input parameters.
Under the assumption that b is small, I like your approach, but I wish you had spelled out the assumption in your first post. Doing so would not have required "paragraphs of unnecessary nerdiness." In fact, you could have made it clear using just two more words. You wrote, "[Y]our risk of hitting the ground is 50% * b + 100% * b (making a minor approximation)." Had you instead written, "Assuming that b is small, your risk of hitting the ground is approximately 50% * b + 100% * b," your assumption and its validity would have been clear. Just two more words (and that's assuming we accept that "b" is actually a word)!
Jay
(This post was edited by jt512 on Apr 27, 2010, 4:43 AM)
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Edit Log:
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Post edited by jt512
() on Apr 27, 2010, 2:02 AM
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Post edited by jt512
() on Apr 27, 2010, 4:34 AM
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Post edited by jt512
() on Apr 27, 2010, 4:43 AM
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