2. The birthday problem poses the following question: how many people do you need in a room so that it is likely that two of them have the same birthday? Assuming that all 366 birthdays are equally likely (they aren't since February 29 th only happens every four years or so, but it makes the problem slightly simpler to understand) we can determine the following: - If there are two people in the room there is a 366365 or 0.9973 probability that they have different birthdays, giving us a 10.9973=0.0027 probablity that they have the same birthday. - If there are three people in the room there is a 366365366364 or 0.9918 probability that all three people have different birthdays, giving us a 10.9918=0.0082 probability that at least two of them have the same birthday. - Continuing this process, it turns out that only 23 people are needed for there to be a probability of at least 0.5 that two people have the same birthday