3 ms·

Even if you shoot only once, you still have a higher chance of hitting something slightly off the middle than the perfect 100/100. And this because that's one p

• tshaddox 11mo ago
  > you still have a higher chance of hitting something slightly off the middle than the perfect 100/100 That's because "something slightly off the middle" is a large group of possible results. Of course you can assemble a group of possible results that has a higher likelihood than a single result (even the most likely single result!). But you could make the same argument for any single result, including one of the results in your "slightly off the middle" group. Did you get 97 heads? Well you'd have a higher likelihood of getting between 98 and 103 heads. In fact, for any result you get, it would have been more likely to get some other result! :D
  • zdragnar 11mo ago
    > But you could make the same argument for any single result Isn't that the point? The odds of getting the "most likely result" are lower than the odds of getting not the most likely result. Therefore, getting exactly 100/100 heads and tails would be unlikely!
    • tshaddox 11mo ago
      But as I said, getting any one specific result is less likely than getting another other possible result. And the disparity in likelihoods is greater for any one specific result other than the 50% split.
    • alwa 11mo ago
      I think the disagreement is about what that unlikeliness implies. "Aha! You got any result? Clearly you're lying!"... I'm not sure how far that gets you. There's probably a dorm-quality insight there about the supreme unlikeliness of being, though: out of all the possible universes, this one, etc...
      • zdragnar 11mo ago
        Let's look at the original quote: > "Remember, if you flip a coin 200 times and it comes heads up exactly 100 times, the chances are the coin is actually unfair. You should expect to see something like 93 or 107 instead". Inverting the statement makes it read something like this: You are more likely to not get 100/100 than you are to get exactly 100/100 ...which is exactly what I was saying. Nobody is arguing that there is a single value that might be more likely than 100/100. Rather, the argument is that a 100/100 result is suspiciously fair.
      • mikkupikku 11mo ago
        Try thinking of it this way: you're in highschool and your stats teacher gives you a homework assignment to flip a coin 200 times. You respect her and don't want to disappoint her, but at the same time the assignment is pointlessly tedious and you want to write down a fake result which will convince her you actually did it. A slightly imperfect split is more likely to convince your teacher that you did the assignment. Intuitively this should be obvious.
• e12e 11mo ago
  Should that be 25% for 97..193 excluding 100?
  • shakow 11mo ago
    “[97; 103] \ {100}” means the interval [97; 103] without the set {100}; so no, still ~30%.