I would appreciate if someone could help me solve and understand these two problems. The first version of this post contained my attempts to solve them, but I have deleted those parts because I saw that I had messed up badly. I really suck at this type of problems, but perhaps someone can show me a good way to approach them. Edit: OK, now I think I get it. If I still think I'm right in 20 minutes I'll probably edit this post again and add my new attempts to solve the problems. Another edit: I have to go to bed, so I don't have time to post the explanations, but the results I get are 10/11 for the first problem and 1/2 for the second. Does that sound right? This is not homework by the way. Oh, and since I'm asking about "Bayesian" probabilities, I would also appreciate if someone could tell me how that word is supposed to be pronounced. Baysian? Buy-eeshan? Buy-eezian? Bay-eezian? I've been wondering about that for years. Problem 1 Two identical boxes. One of them contains 10 balls numbered 1-10. The other one contains 100 balls numbered 1-100. You don't know if the box on the left contains 10 or 100. You use a coin flip to choose one of the boxes and ask a friend to pick a ball at random from it. The ball he picks has the number 9 written on it. What is the probability that the box you chose contained 10 balls? Problem 2 Two identical buildings. Both of them contain 100 rooms numbered 1-100. 110 people are blindfolded and randomly put into rooms 1-10 of building A, and rooms 1-100 of building B. You're one of those people, and you're told that your room number is 9. What's the probability that you're in building A?