Earlier quoted context omitted.
You know, I never know what to make of that logic - what if that tiny probability was exactly this one time? It's not like we saw it happen twice, and it could happen at some point. To my gut it seems you can't really know until you have other positive or negative observations. I wonder if someone has compiled a list of very improbable events that have been observed.
Wow - this has got to be my most downvoted comment. I can't edit the original anymore, so here's my update: I guess the harsh reaction came from the fact that I didn't define the scope very well: My question wasn't in reference to M-R specifically, just in general. I understand that in this case it makes sense to look at likelier causes (see Sharlin's response). My point was that it's interesting to look at what happ…
Because it isn't true that the probability of any given person being struck by lightning is 1/10000. For instance, the internet says that men are around 4 times as likely to be struck by lightning as women. Rather, what's true is that the likelihood of a randomly selected person being struck by lightning is 1/10000. Each individual person has a different likelihood to be struck. I don't know how to calculate it for Roy, but given that he's been struck 7 times I'm sure it's way higher than 1/10000.
> That also makes me think - is there even such a thing as the "true" or inherent probability of an event happening?
I love when people email me after reaching an enlightenment.
There was a probability question that drove me nuts until I figured out what was going on. The question is "A woman has two children. One of her children is a boy. What is the probability that she has two boys?".
The question isn't well defined, because it matters how you learned that one of her children is a boy.
If you asked her "what is the gender of your oldest child?", and she says it's a boy, then the probability that she has two boys is 1/2.
But if you asked her "do you have at least one boy?", and she says yes, then the probability that she has two boys is 1/3.
I don't know what the lesson here is. Probability is hard? Always ask about the experiment?
> is there even such a thing as the "true" or inherent probability of an event happening?
The probability of something depends on what you know. What's the chance that Roy will be struck by lightning tomorrow? If you don't know who Roy is, you might say 1/(10000 * 28000) (where 28000 days is the average human lifespan.). If you do know Roy's history, you'll probably bump that estimate up quite a bit. But if you look up the weather in his park tomorrow and see that it will be sunny all day, the probability will go back down close to zero.
Some things are so hard to know they might as well have an inherent probability, though. If you roll a die, no one's going to predict the outcome of the roll, so we might as well say it's inherently got a 1/6 chance of rolling a 5. And if you shine a photon at a half-silvered mirror, it's actually impossible to predict which way it will go, so I guess that really does have in inherent probability.
You've got to watch out for your probability estimates being wrong, though. I thought the probability of my friend flipping a coin and getting heads was 1/2, until he demonstrated that he could flip heads 10 times in a row.
> edit: Or maybe it's the law of large numbers - given enough "trials" or in this case lightning events with people around, even something with an absurdly small probability is bound to happen eventually. But then why do we never factor that in and always just call it a day with 10000^7?
Because even with 10 billion people, each living a billion days, and having a billion things happen to them in a day... well coincidentally that's exactly 10^28=10000^7, so never mind.