5 ms·

Is the reasoning here correct?

by Nabati 5y ago

totony 5y ago
1 in ~10 million seems to be the average risk of an american to die from air plane, so, in your lifetime (100 years, if you live to 100 - average lifespan is 80 it looks like), that goes up to 1-(9,999,999/10,000,000)^100 ~ 1 in 100k Since that number is about the average risk of an american to die (and not the risk per flight), using it to calculate the risk per flight is erroneous I think?
- pcurve 5y ago
  Actually the 1 in 10 million figure I used is based on number of fatal crash per flight. I thought it was roughly 1 in 10 million flights ending in fatal crash, but that was couple years ago. It's actually more like 1 in 3.7 million flights. so if you take 100 of those flights, I figured the odds would be 1 in 37,000. Anyway, happy to be corrected.
  - totony 5y ago
    You might be right, but from cursory look [1] [2], there were 300 fatalities / 5000 millions passenger ~ 1 / 17 millions for 2019 so your probability of dying from one flight (all of the world considered - way lower for US afaics) looks to be 1 in 17 millions in 2019 [1] https://www.statista.com/statistics/263443/worldwide-air-traffic-fatalities/ https://www.statista.com/statistics/263443/worldwide-air-tra... [2] https://www.statista.com/statistics/564717/airline-industry-passenger-traffic-globally/ https://www.statista.com/statistics/564717/airline-industry-...
mathieuh 5y ago
No they're using the gambler's fallacy, each flight you take is unaffected by any flight you've taken previously. Flying a load of times isn't reducing the denominator.
- konstmonst 5y ago
  Flying increases Cancer risk because of Cosmic Radiation. Solar Flares while flying are extremely dangerous.
- pcurve 5y ago
  Isn't gambler's fallacy more about expectation of future result skewing based on past outcome? If there's a very dangerous airplane ride that results in 10% of all flights ending in crash, if you take that plane 10 times, wouldn't you expect 1 crash on average?
  - mathieuh 5y ago
    Looks like I'm wrong judging by the other comments, that'll learn me to not make comments on things I'm not sure about...
- freyir 5y ago
  It’s not the gambler’s fallacy since they’re treating each flight as an independent event: Probability of dying on one flight: 1/10,000,000 Probability of surviving one flight: 1-1/10,000,000 = 9,999,999/10,000,000 Probability of surviving 100 flights: (9,999,999/10,000,000)^100 Probability of not surviving 100 flights: 1-(9,999,999/10,000,000)^100 ~ 1/100,000. I don’t know if the initial assumption of 1/10,000,000 survival rate is accurate, but the math is correct. And when you have a probability that’s very small, you can skip all that and approximate by multiplying the probability by the number of events: 1/10,000,000 * 100 = 1/100,000. That’s thanks to the binomial approximation.

Is the reasoning here correct?

by Nabati 5y ago

Is the reasoning here correct?

1 in ~10 million seems to be the average risk of an american to die from air plane, so, in your lifetime (100 years, if you live to 100 - average lifespan is 80 it looks like), that goes up to 1-(9,999,999/10,000,000)^100 ~ 1 in 100k Since that number is about the average risk of an american to die (and not the risk per flight), using it to calculate the risk per flight is erroneous I think?

pcurve 5y ago
Actually the 1 in 10 million figure I used is based on number of fatal crash per flight. I thought it was roughly 1 in 10 million flights ending in fatal crash, but that was couple years ago. It's actually more like 1 in 3.7 million flights. so if you take 100 of those flights, I figured the odds would be 1 in 37,000. Anyway, happy to be corrected.
- totony 5y ago
  You might be right, but from cursory look [1] [2], there were 300 fatalities / 5000 millions passenger ~ 1 / 17 millions for 2019 so your probability of dying from one flight (all of the world considered - way lower for US afaics) looks to be 1 in 17 millions in 2019 [1] https://www.statista.com/statistics/263443/worldwide-air-traffic-fatalities/ https://www.statista.com/statistics/263443/worldwide-air-tra... [2] https://www.statista.com/statistics/564717/airline-industry-passenger-traffic-globally/ https://www.statista.com/statistics/564717/airline-industry-...

mathieuh 5y ago

No they're using the gambler's fallacy, each flight you take is unaffected by any flight you've taken previously. Flying a load of times isn't reducing the denominator.

konstmonst 5y ago
Flying increases Cancer risk because of Cosmic Radiation. Solar Flares while flying are extremely dangerous.
pcurve 5y ago
Isn't gambler's fallacy more about expectation of future result skewing based on past outcome? If there's a very dangerous airplane ride that results in 10% of all flights ending in crash, if you take that plane 10 times, wouldn't you expect 1 crash on average?
- mathieuh 5y ago
  Looks like I'm wrong judging by the other comments, that'll learn me to not make comments on things I'm not sure about...
freyir 5y ago
It’s not the gambler’s fallacy since they’re treating each flight as an independent event: Probability of dying on one flight: 1/10,000,000 Probability of surviving one flight: 1-1/10,000,000 = 9,999,999/10,000,000 Probability of surviving 100 flights: (9,999,999/10,000,000)^100 Probability of not surviving 100 flights: 1-(9,999,999/10,000,000)^100 ~ 1/100,000. I don’t know if the initial assumption of 1/10,000,000 survival rate is accurate, but the math is correct. And when you have a probability that’s very small, you can skip all that and approximate by multiplying the probability by the number of events: 1/10,000,000 * 100 = 1/100,000. That’s thanks to the binomial approximation.