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#101
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#102
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"George Patterson" wrote in message ... Jose wrote: But you would never say "the Appalachian ranges." For the same reason, you should never say "the Sierras" when you're talking about the Sierra Nevada. But we say "the Appalachians". And it would be correct to say "the Nevadas." But not "the Sierras." George Patterson I prefer Heaven for climate but Hell for company. Correct or not. I live out here and if you said in conversation: I went hiking last weekend in the Sierra. or I think I will go skiing next week in the Sierra or Take I80 over the sierra. You would sound kind of goofy to a local. Howard |
#103
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1. The probability of experiencing an engine failure (or any other
improbable event for that matter) AT SOME POINT IN YOUR FLYING CAREER goes up the more you fly. It goes up monotonically but nonlinearly according to the formula 1-(1-P)^N, which asymptotically approaches 1 as N gets large. I have a feeling everyone in this discussion is talking past each other. However, I'll still pick a nit (since after all, this is usenet). Probability deals =only= with events whose outcome is not known or not taken into account. If I take any random 10,000 hours, the probability of some occurance (like an engine failure) is the same. Let's say the probability over 10,000 hours is 70%. If I have =already= flown 9,999 hours without a failure, it is =not= true that my chance of failure on the last hour is 70%. Likewise, if I have already flown those 9,999 hours and already had three engine failures, the chance of having another in that last hour is =not= zero nor is it negative ("to make up for the extra failures"). It is the same as the probability of a failure on the =first= hour. HOWEVER... the chance that, OVER THOSE 9,999 HOURS flown =plus= the one not flown, I would =either have an engine failure shortly, =or= look over my logbook and find that I already had one, would be the original 70%. The key here is including those flown hours without regard to whether or not there was a failure there - iow as if we did not know the result. If you eliminate the hours flown because their outcome is known, then you can only (correctly) apply probability to the unflown hours. This is (of course) a different question from the one that says "Here's my logbook. It has 10,000 one-hour flights in it. I had one engine failure." and then, as one thumbs through the book saying "not this one... not this one..." the chance of coming across a flight with an engine failure =does= increase - because in this case an engine failure is =guaranteed=. (it already happened). Running out of fuel is not my idea of "engine failure". If the fuel pump breaks and thus all four engines quit, did you have an engine failure? Jose r.a.owning and r.a.student trimmed. I don't follow them. -- Nothing is more powerful than a commercial interest. for Email, make the obvious change in the address. |
#104
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#105
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#106
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#107
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"Ron Garret" wrote in message
... In article , wrote: I think the implication, with all due respect, in the way you worded your post, is that the probability is increasing as you flying time is increasing. It depends on what you mean by "the probability". There are two different probabilities being discussed: there is the probability of a failure on any particular flight, which doesn't change, and there is the cumulative probability of experiencing failure on some flight, which does change (it increases with each flight). This is clearly not the case, as I think we all now agree. There is also the probability (that Peter (I think) proposed) stated as a cumulative probability in terms of an arbitrary large number of trials (flights, or hours, or whatever). If you convert this to a probability of occcurence with a lower number of trials (flights, or hours, or whatever) that probability will be lower. Looked at it this way, if the probability of an 'occurrence sometime in (the remainder of )one's career is known, then as the career progresses, the probability of 'an occurrence sometime (in the remainder of) one's career diminishes from that value. This is a direct consequence of 1) the premises (accepted by all here, apparently) that - the probability for any given trial (hour, flight, or whatever) is assumed to be independent of any other given trial (hour, flight or whatever) and - the probability is assumed to be the same for each such trial, and 2) the assertion that the probability of an occurrence over n trials is (1-(1-p)^n, where p is the probability of occurence in a single such trial. Its the same problem worked back to front (or front to back, depending on your point of view): i.e.: Let p2 be the probability of an occurence in n2 trials, and let p1 be the probability of an occurence in n1 trials, if n1 n2, then p1 p2. If you *start* with p1, as you consider an increased number of trials the probability will increase, if you *start* with p2 and consider a decreased number of trials, the probability will decrease. Your statement is ambiguous because you don't say which probability you're referring to. Yes. The logical conclusion is determined from the premises used. You only get out of it what you put in. Every day is a new day, and N gets reset to zero. Not quite. Every day is indeed a new day, but with every flight N is incremented by one. It depends on upon from which premise you started. If you're considering your probability in terms of occurences per N trials, you might change N if you start out with it being 'the number of trials in my entire career', but the probability of an occurence 'in the next N trials' otherwise doesn't need any change in N from day to day. But 'the number of trials in my career' is moot in the first place, and I'd argue that arbitrarily specifiying the number of trials that are 'going to occur' in your career is equally problematic, as is coming up with such a probability in the first place. The best you can get out this argument, I think, starting out with a guess for the cumulative probability of the 'entire carreer', is a qualitative 'probability is decreasing' as the career progresses, and you can't really ever quantitatively say how much. |
#108
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In article P68Ud.515993$8l.368458@pd7tw1no,
"Ron McKinnon" wrote: as the career progresses, the probability of 'an occurrence sometime (in the remainder of) one's career diminishes from that value. Yes, but only because N is lower. Whatever N is, after every flight N is 1 less than it was before. But 'the number of trials in my career' is moot in the first place, That is arguable. As a precise number you're probably right. But in broad brushstrokes you can decide, e.g. never to try something, to try something once and then never again, to try something a dozen times in your lifetime, to do something once a month, once a week, once a day, or multiple times a day. Each of these choices entails a monotonically increasing risk of encountering certain kinds of disasters over your lifetime. My personal risk tolerance works out something like this: Things I'm not willing to try even once: heroin, motorcycle racing Things I'm willing to try once in my lifetime and never again: going into space (assuming I ever have the opportunity) Things I'll do a dozen times: aerobatics Once a month (on average): skiing Once a week: Flying GA aircraft Once a day: getting out of bed in the morning :-) Multiple times a day: driving on the freeway, eating sushi :-) rg |
#109
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wrote in message
... [...] the chance is actually only 75%. How so? The probability of both engines failing is .25, I agree, but I'm talking a failure of either engine. I am too. What chance do YOU think you have of having a failure of either engine, if not 75% (in this example)? If the chance of an engine failure is 50% (0.5), then the chance of either engine failing when you have two engines is 1-(0.5)*(0.5). 75%. The probability of both engines failing is indeed only 25%. The probability of EITHER engine failure is 75%. You need to do the subtraction because the chance of an engine failure is actually the opposite of the chance of completing a flight without an engine failure. To make the flight successfully without either engine failing requires BOTH engines to not fail, and the way to calculate that is to multiply the chances of each engine failing (which in this case is just two engines, with identical chances). The chance of you completing the flight without a failure is 25% (50% * 50%), so the chance of an engine failure on the flight is 75%. Pete |
#110
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"Ron Garret" wrote in message
... [...] If you think about it, there is absolutely no difference in the risk calculation between making one flight with four engines and four flights with one engine The difference is that when you make a flight with four engines, you know up front that you're carrying four engines. The calculation based on making four flights with one engine is only useful when you know in advance you're making four flights. I certainly hope to make at least four more flights during my flying career, but it's not certain that I will. Sorry you can't see the difference. It's a crucial element to the question of whether it makes sense to worry about the cumulative odds of an engine failure. Pete |
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