Fascinating mental problem: Sleeping Beauty.
Say Sleeping Beauty, who forgets that she woke up after she goes back to sleep, will be awakened either only on Monday, or on Monday and Tuesday. Prince Charming will flip a coin to determine which. Heads, wake twice, tails, wake once.
So Sleeping Beauty awakens, and Prince Charming offers to bet her a Coke that the coin came up tails. Should she take the bet?
Well, when she awakens, it's either the first day of the heads series, the only day of the tails series, or the second day of the heads series. So of the three things that could be going on, two of them mean that the coin came up tails. This would seem to indicate that the bet would be wise.
But a coin always has, give or take (there is a slight edge to one side), a 50-50 rule as to outcome. The condition of her waking up doesn't change that.
Sleeping Beauty's only chance for wisdom would to realize that it would be impossible for her to know what was going on when she awakened.
The moral of the story: If you can't know if any of the things that might be going on are actually the case, it is best to build your world around the things that you do know.