as for two people, times 363/365. so the probability that three people will share a birthday is 1 - (364/365) * (363/365). notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining. we keep adding people until the %age is greater than 50%. when we have 23 people the %age is 50.729%. 