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In statistics there's a slight difference between something that happens 100% of the time and something that always happens. Or rather just because something h

In statistics there's a slight difference between something that happens 100% of the time and something that always happens. Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time. They may also have been referring to the fact that picking a random number over the whole number line is not that as simple as it sounds since the uniform distribution doesn't exist.

JadeNB 8y ago
> Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time. There is definitely a mathematical sense in which events with probability 0 can happen, but I don't know of any 'real-world' setting, e.g., in statistics, in which we correctly assign an event a probability of 0 (rather than just "too small to distinguish from 0") and yet find it happening. Could you give an example?
- Koshkin 8y ago
  Pick a random point on the real line. It has happened. The probability of that happening was (and still is) zero. The mathematical sense you are referring to is "existence": the number you have picked does exist, but the probability of it being selected is zero.
  - JadeNB 8y ago
    > The mathematical sense you are referring to is "existence": the number you have picked does exist, but the probability of it being selected is zero. Yes, I know. However, contravariant said (https://news.ycombinator.com/item?id=18174774 https://news.ycombinator.com/item?id=18174774): > In statistics there's a slight difference between something that happens 100% of the time and something that always happens. > Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time. I took this to be a claim that there was a 'real-world' sense (or as real-world as statistics is), not just a strictly mathematical sense, in which events with probability 0 happen "all the time", and I was wondering what this sense (not the mathematical sense) was.
    - Koshkin 8y ago
      It's just the converse: the probability of not picking the given number was (and still is) 100%, but you did pick it, so what "had to" happen with 100% probability, didn't. (Maybe that's the meaning of the perceived difference between the real world and statistics. Playing a lottery doesn't make sense, but people do win!)

JadeNB 8y ago

> Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time. There is definitely a mathematical sense in which events with probability 0 can happen, but I don't know of any 'real-world' setting, e.g., in statistics, in which we correctly assign an event a probability of 0 (rather than just "too small to distinguish from 0") and yet find it happening. Could you give an example?

Koshkin 8y ago
Pick a random point on the real line. It has happened. The probability of that happening was (and still is) zero. The mathematical sense you are referring to is "existence": the number you have picked does exist, but the probability of it being selected is zero.
- JadeNB 8y ago
  > The mathematical sense you are referring to is "existence": the number you have picked does exist, but the probability of it being selected is zero. Yes, I know. However, contravariant said (https://news.ycombinator.com/item?id=18174774 https://news.ycombinator.com/item?id=18174774): > In statistics there's a slight difference between something that happens 100% of the time and something that always happens. > Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time. I took this to be a claim that there was a 'real-world' sense (or as real-world as statistics is), not just a strictly mathematical sense, in which events with probability 0 happen "all the time", and I was wondering what this sense (not the mathematical sense) was.
  - Koshkin 8y ago
    It's just the converse: the probability of not picking the given number was (and still is) 100%, but you did pick it, so what "had to" happen with 100% probability, didn't. (Maybe that's the meaning of the perceived difference between the real world and statistics. Playing a lottery doesn't make sense, but people do win!)