There are so many questions on probability that there's a low probability of me finding a duplicate in the list, if there even is one.
And I can't figure out a good title, so feel free to edit!
Situation: There is a set of sets, and their sizes are different. For example, a library is a set of books, and each book is a set of pages, but the number of pages varies. Here are two ways to pick a page at random:
- Construct a set of all pages, i.e., of tuples containing all possible (book,page), and then a random pick from there.
- Randomly pick a book, then randomly pick one of its pages.
Does every page in the library have the same probability of being chosen in both scenarios? Or does the second give pages in shorter books a greater probability? (Intuitively, the latter seems likely to me, but intuition is often wrong.)