What is each of their prior probabilities for this setup being true? Bob, knowing that he was selected for his unusual results, can pretty happily disregard them. If you win a lottery, you don’t update to believe that most tickets win. Bob now knows of 100 samples (Al’s) that relate to the prior, and accepts them. Bob’s sampling is of a different prior: coin flipped, then a specific resulting sample will be found.
If they are both selected for their results, they both go to 50⁄50. Neither one has non-selected samples.
What is each of their prior probabilities for this setup being true? Bob, knowing that he was selected for his unusual results, can pretty happily disregard them. If you win a lottery, you don’t update to believe that most tickets win. Bob now knows of 100 samples (Al’s) that relate to the prior, and accepts them. Bob’s sampling is of a different prior: coin flipped, then a specific resulting sample will be found.
If they are both selected for their results, they both go to 50⁄50. Neither one has non-selected samples.