At first glance this seemed like it might have something to do with the birthday paradox (http://en.wikipedia.org/wiki/Birthday_paradox) but that only says something about the probability that a pair of people out of a group has the same birthday, not the probability that a single person has the same birthday as someone in the group.
Now, if the bet were "I win $x if any two people at the party have the same birthday, you win $x if none do" then that is exactly the birthday paradox. If there are 23 or more people at the party then the probability is greater than 50% and you should take the bet.
So unless I'm missing something it's either a stupid question or a trick question.
Now, if the bet were "I win $x if any two people at the party have the same birthday, you win $x if none do" then that is exactly the birthday paradox. If there are 23 or more people at the party then the probability is greater than 50% and you should take the bet.
So unless I'm missing something it's either a stupid question or a trick question.