tag:blogger.com,1999:blog-9124539381685751273.post4969893178929000222..comments2023-06-19T04:35:06.263-07:00Comments on Skeptic's Play: Solution to "Flipping coins in parallel universes"millerhttp://www.blogger.com/profile/05990852054891771988noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-9124539381685751273.post-13450606131832375162008-05-21T11:46:00.000-07:002008-05-21T11:46:00.000-07:00I see you've picked up on the slight ambiguity in ...I see you've picked up on the slight ambiguity in Universe 1. If Leela has other possible answers, the probabilities could be skewed. For instance, perhaps she had a probability of saying "both coins are the same, but I'm not saying what they are".<BR/><BR/>The idea for the two universes came from the fact that the classic puzzle is often stated ambiguously. It is not clear whether it should be interpreted like Universe A or Universe 1, though 1/3 is the expected answer.<BR/><BR/>I think the answer to your rigorously stated variation is 2/5.millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-69179602782012238242008-05-21T10:08:00.000-07:002008-05-21T10:08:00.000-07:00I think the key with the second problem (I can't k...I think the key with the second problem (I can't keep track of which one is A and which is 1) is to know how Leela chooses what information to give. She could have just as easily decided "I'll say at least one is tails unless I am forced not to", in which case the probability would again be 1/3. In the absence of information about her decision procedure, I suppose one would have to think of all possible ways she could decide what information to give, find the probability that both are tails in each case, and figure out the probability that she would choose that particular way of providing the information.<BR/><BR/>So here's a variation for you: Leela flips two coins. Then she picks from two options: 1) She will declare that at least one coin is tails unless both are heads, or 2) She will pick the coin on the left and say that at least on coin is [whatever that coin is]. To decide between these two methods, she flips a (different) coin.<BR/>Given that Leela says "At least one coin is tails", what is the probability that both are tails?Anonymousnoreply@blogger.com