If I pick an interval uniformly from a pool of intervals of which 95% contain the true value, it has a 95% chance of containing the true value.
Just like if I pick a ball from a bag of balls of which 50% are red, it has a 50% chance of being red.
If I pick an interval uniformly from a pool of intervals of which 95% contain the true value, it has a 95% chance of containing the true value.
Just like if I pick a ball from a bag of balls of which 50% are red, it has a 50% chance of being red.
If you pick a ball from a bag of balls of which half are fuzzy and half are smooth, then before picking the ball, there is indeed a 50% chance that you will pick a fuzzy one. But once you pick it and have it in your hand and can feel the texture, are you still going to say “there’s a 50% chance that this specific ball I am holding is fuzzy because half of the balls in there were”?