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The REAL odds of being in a plane crash
So I set out to find the actual odds of being involved in a commercial airliner crash on a per flight basis. I thought this would be easy to find. What I found was a whole lot of rhetoric about "your more likely to die on the way to the airport" and "you're safer up in the air than you are down here" type of answers, but I had a very hard time locating any actual numbers or statistics.
I kept searching When I actually found the "statistics" that back these attitudes and expressions I was shocked at how flawed and purposely skewed these statistcs were. The "official" statistic that always seems to be thrown out there is this 1 in 11 million chance of being in a plane crash per person, per year. And the way that they arrive at this number is just ridiculous. They divide the number of crashes in a year into the TOTAL POPULATION, and boom. 1 in 11 million. However, most people don't fly all that often, if at all. So that doesn't mean anything to someone who travels alot. I concluded that there is millions and millions of dollars invested into making the average american feel safe on an airplane, and that these extremely flawed statistics that are put out there by supposedly "official" sources are pretty much propaganda, and I was determined to have my question answered. What are the odds that MY specific flight crashes. So I did some research and crunched the numbers and here is what I came up with: average number of US commercial flights per year divided by average number of US commercial crashes per year = odds of your specific flight crashing SO 9,748,551(national airtraffic controllers association) divided by 36.05(national transportation safety board) = 1 in 270,417 1 in 270,417 that your flight goes down. And that's if your taking just one flight. If you take a round trip, it's 2 x 1/270,417. If you take a round trip with a connector flight each way, then it's 4 x 1/270,417. SO odds of being in a crash after 10 flights = 1 in 27,041 100 flights = 1 in 2,704 200 flights = 1 in 1,352 These don't sound nearly as appealing as that 1 in 11,000,000, do they? Anyways I'm thinking of organizing all of this into an article, and the reason I posted this here is because I would like you math guys out there to "check my work" and see that my numbers are correct, or if you can add anything to my numbers or argument. |
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Well, technically you cannot just add them up. So for 2 flights you need to figure the probability of NOT crashing. Which is 270416/270417. Then take that number to the 2nd power. .999996^2. Then subtract that result from 1. 1 - .999993 = .00000739597.
For 10: .000369738 For 100: .036311108 For 200: .137546825 But I don't really know what to make of this. What year's did you include in your calculation of the average? It might be better to know the number of flights and crashes for each year separately. |
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http://www.ntsb.gov/aviation/Table5.htm |
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As Sherman noted, your math is wrong.
The formula should be: (1-x)^y = chance of no crash where x is the chance of crashing (1/270417), and y is the number of trials (flights). Here is what I get: assuming 1 in 270,417 is right 1 flight: 99.99963% no crash Roundtrip = 99.99926% no crash roundtrip with connector (4 flights) = 99.99852% no crash 10 flights = 99.99630% no crash 100 flights = 99.96303% no crash 200 flights = 99.92607% no crash 6000 flights = 97.80563% no crash 187438 flights = 50.00008% no crash So, don't ever take a 187,439th flight. You are sure to die. |
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Here is a hastily drawn graph of the function for variously selected numbers of flights. You would need close to 1M to have a 95% chance of being in a crash...which is nice I suppose.
http://img191.imageshack.us/img191/4945/planecrasha.jpg |
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I would be interested in knowing what is included in "accidents". |
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Remember that all donīt die in every "crash". Have you taken that into account?
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Yes, there is a difference between being in a crash and dying. I sort of assumed the OP meant being in a crash and dying. Clearly he just meant being in an "accident" which is unlikely to just include crashes. It probably includes two planes bumping into one another while taxiing or something.
In any case, here are two graphs with the Fatality data. http://img717.imageshack.us/img717/4...edeathdata.jpg As the first graph makes clear, the probability of being in a fatal plane accident (fatal accidents per departure), has been on a decline since 1989. This suggests that simply averaging the results from 1989-present is a mistake. However, for simplicity I did it anyway (p = .000000637) and plotted the probability of being in a fatal accident as a function of the number of flights taken. So even after 1M flights, you would only have a 30% chance of being in a fatal plane accident. |
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What are the odds for an average flight pilot to be in a accident during his career (respectively to "not be among us anymore" due to a flight accident)?
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Can anyone turn these into statistics? I.E. "1 in xxx"
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the 6000 was supposed to represent a pilot halfway through his career. and the last number: someone who wants to be more than 50% sure they don't end up in a crash. turning the numbers into "statistics": use division. |
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They might be counting things like the failed Christmas bombing in Detroit or the pilots that were playing (online poker?) on their laptops and overshot their destination. Do the stats detail the incidents in a year? |
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The OP seems to think that many of these accidents involve serious, but non-fatal injuries. However, I am not sure I believe that. How many people in the Hudson river landing (in which that pilot became famous) were seriously injured? I don't recall hearing about any. Yet I am certain that is reported as an "accident" and probably a fairly major one by airline standards. |
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As defined by the NTSB, this is an occurrence associated with the operation of an aircraft where as a result of the operation of an aircraft, any person (either inside or outside the aircraft) receives fatal or serious injury or any aircraft receives substantial damage. The occurrence is also not caused by the deliberate action of one or more persons and that leads to damage or injury. The NTSB definition, which is also used by the FAA, divides accidents into four categories: 1.Major - an accident in which a 14 CFR 121 aircraft was destroyed, there were multiple fatalities, or there was one fatality and a 14 CFR 121 aircraft was substantially damaged. 2.Serious - an accident in which there was either one fatality without substantial damage to a 14 CFR 121 aircraft, or there was at least one serious injury and a 14 CFR121 aircraft was substantially damaged. 3.Injury - a nonfatal accident with at least one serious injury and without substantial damage to a 14 CFR 121 aircraft. 4.Damage - an accident in which no person was killed or seriously injured, but in which any aircraft was substantially damaged. The failed christmas bombing, and the pilots overshooting they're destination would not be recorded as accidents. And neither would a runway bump unless it caused substantial damage. These would be recorded as incidents, and not included in the afformentioned accident statistics Incident An occurrence, other than an accident, associated with the operation of an aircraft that affects or could affect the safety of operations. |
Re: The REAL odds of being in a plane crash
Can anyone turn these into statistics/ratios? I.E. "1 in xxx"
Quote: 1 flight: 99.99963% no crash Roundtrip = 99.99926% no crash roundtrip with connector (4 flights) = 99.99852% no crash 10 flights = 99.99630% no crash 100 flights = 99.96303% no crash 200 flights = 99.92607% no crash 6000 flights = 97.80563% no crash 187438 flights = 50.00008% no crash anyone? |
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1 flight: 99.99963% no crash = 1 in 270.270 10 flights = 99.99630% no crash = 1 in 27.027 100 flights = 99.96303% no crash = 1 in 2.705 200 flights = 99.92607% no crash = 1 in 1.353 6000 flights = 97.80563% no crash = 1 in 46 187438 flights = 50.00008% no crash = 1 in 2 |
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Here's the link. And remember, keep those seat-belts buckled. http://www.ntsb.gov/NTSB/query.asp |
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