# Probability Conundrum

<p>So, a woman gets into a plane crash and survives it.</p>

<p>Since it is very unlikely that she will be in another plane crash in her life because of the safety of planes, I ask you this. Is it safer to travel in the same plane as her, compared to another plane? Or is the probability the same?</p>

<p>The probability of crashing with or without her is exactly the same.</p>

<p>For example, let’s say the probability of crashing is 1/10 (yeah yeah no need to use actual numbers to prove a point.) </p>

<p>After her first crash, she still has a 1/10 chance of crashing again, but the probability of her crashing two times to begin with is 1/100.</p>

<p>Unless she is a terrorist, then this all gets thrown out the window.</p>

<p>This isn’t a conundrum at all. Unless you believe she was the cause of the first crash - attempted hijacking, bad karma, weight, whatever - the probability of another plane crashing is independent of her presence.</p>

<p>Independent events.</p>

<p>Her probability is the same every time she gets on a plane. She has no control over the outcome.</p>

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<p>Independence is kind of an idealization though. If she flew before on a plane that crashed, it’s more likely that she was flying a route that would be more susceptible to plane crashes (for whatever reason), and thus it’s more likely that the current flight is on a route that’s susceptible to plane crashes.</p>

<p>Now this “logic” is based only on the condition that she was in a plane crash before. If you add more info, like knowing what her previous route was (and by extension, whether it was more susceptible to plane crashes) or knowing what the current route is, then the probability could change. I would also add that if “changing planes” constitutes merely getting on a different plane on the same route, then the probability would get a tiny bump simply based on the tiny chance that she caused the previous crash and would be more likely to cause another crash than some other random passenger.</p>

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Eh, I suppose you could perform a chi-square independence test on data for plane crash survivors. If you could find said data. Otherwise, this is all just speculation.</p>

<p>I don’t know that I would trust it to adequately distinguish between a tiny correlation and none. Probability of a type II error seems pretty big there.</p>

<p>I should probably add that if you’re afraid to get on a plane just because one woman on the plane had previously been in a plane crash, it may be worth visiting a therapist.</p>