carrot99, it does not work like that. What you have to do is, starting with one person, work out the probability that another person does not have the same birthday (364/365) and then keep adding people, calculating the probabilities and multiplying them. Your calculation should be (364/365)x(363/365)x(362/365)x... etc. When this product drops below...
what you are calculating is the probability that each additional person has a different birthday from all those already present. Once this drops to less than 0.5, it means that it is more than 50% likely that two people do share the same birthday
yes, because the probability that the 366th or 367th person does not share a birthday with anyone else is now 0/365 (or 0/366) - there are no possibilities left - so the overall product becomes zero.