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.

Flying increases Cancer risk because of Cosmic Radiation. Solar Flares while flying are extremely dangerous.

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?

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.