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For a long time now I've been thinking about something I find odd about probabilities. For example, let's say that I win the lottery, something that is extremely unlikely. What is the probability that I will be struck by lightning? The odds of someone winning the lottery and getting struck by lightning are extremely low because both events are unlikely, so for them to both happen to one person is extremely improbable. However, just because I've won the lottery doesn't mean the chances of me getting struck by lightning are any lower. If the probability of getting hit by lightning is 1 in 1000000 (made up statistic) for everyone, my having won the lottery doesn't change that, therefore the chances of me being hit is still 1 in 1000000. Which is the probability of me getting hit? 1 in 1000000 or the likelihood of me winning the lottery and getting hit by lightning (which would be lower than 1 in 1000000).

As another example that is related, would my reasoning be correct that if I purposely got myself into a serious car accident, but not fatal, I should be able to go back on the road with less fear as it is unlikely for me to get into two serious car accidents during my life time? This doesn't seem right, but technically aren't the odds of me getting into another serious accident lower because the odds of me getting into two accidents is really small?

I don't know if that makes much sense as I didn't articulate my confusion very well, but I have been wondering about this for a while, so as a summary question: Does the probability of an event occurring change because of past, unrelated events?

As another example that is related, would my reasoning be correct that if I purposely got myself into a serious car accident, but not fatal, I should be able to go back on the road with less fear as it is unlikely for me to get into two serious car accidents during my life time? This doesn't seem right, but technically aren't the odds of me getting into another serious accident lower because the odds of me getting into two accidents is really small?

I don't know if that makes much sense as I didn't articulate my confusion very well, but I have been wondering about this for a while, so as a summary question: Does the probability of an event occurring change because of past, unrelated events?

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