Andy, Bob, and Charley have all been serving time for grand theft auto. According to prison scuttlebutt, the warden plans to release two of the three next week. They all have identical records, so the two to be released will be chosen at random, meaning that each has a two-thirds probability of being included in the two to be set free. Andy, however, is friends with a guard who will know ahead of time which two will leave. He offers to tell Andy the name of one prisoner other than himself who will be released. Andy, however, declines the offer, believing that if the learns the name of one prisoner scheduled to be released, then his chances of being the other person set free will drop to one-half (since only two prisoners will be left at that point). Is his concern justified?
Andy, Bob, and Charley have all been serving time for grand theft auto. According to prison scuttlebutt, the warden plans to release two of the three next week. They all have identical records, so the two to be released will be chosen at random, meaning that each has a two-thirds probability of being included in the two to be set free. Andy, however, is friends with a guard who will know ahead of time which two will leave. He offers to tell Andy the name of one prisoner other than himself who will be released. Andy, however, declines the offer, believing that if the learns the name of one prisoner scheduled to be released, then his chances of being the other person set free will drop to one-half (since only two prisoners will be left at that point). Is his concern justified?
Solution Summary: The author explains that Andy's concern is justified, but not justified. If Charley and Bob are set to be released, the guard has a 50% chance of telling Andy that Bob was released.
Andy, Bob, and Charley have all been serving time for grand theft auto. According to prison scuttlebutt, the warden plans to release two of the three next week. They all have identical records, so the two to be released will be chosen at random, meaning that each has a two-thirds probability of being included in the two to be set free. Andy, however, is friends with a guard who will know ahead of time which two will leave. He offers to tell Andy the name of one prisoner other than himself who will be released. Andy, however, declines the offer, believing that if the learns the name of one prisoner scheduled to be released, then his chances of being the other person set free will drop to one-half (since only two prisoners will be left at that point). Is his concern justified?
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