ABSTRACT
More precisely, we divide the period from 8 to 4 into two four-hour intervals: (8, 12] and (12, 4), with both intervals open on the left. (If the first were not open on the left, the paradox would not arise, because the man could arrive at the stroke of 8.) In consequence, if the Cable Guy arrives precisely at noon the morning interval wins. In the absence of further information, it looks as if his arrival in either interval is equally likely. (The fact that the morning interval is closed on the right does not make it any longer.)
Suppose you bet on the morning interval. Whenever the man arrives, some part of the morning interval must have passed. Whenever he arrives there will be an earlier time at which the afternoon bet is preferable, since the afternoon interval will be longer than what remains of the morning interval after that time. On the other hand if you bet on the afternoon interval there will be no time before the arrival at which you should rationally prefer the morning bet.
