Generate Samples.

A very famous birthday problem makes its rounds in almost every introductory probability class. The question posed is: “What is the fewest number of people that can be assembled in a room so there is a probability greater than 0.5 of at least one duplicate birthday, given that the year of birth is not considered.” Many neglect February 29th (leap year) as a birthday, because it complicates the initial analysis. If we neglect February 29th as a birthday, assume that all birthdays are equally likely, and therefore, the probability for any birthday is 1/365 . We will also assume that the people assembled have birthdays that are unrelated, i.e. independent. Independence means that knowing one birthday does not give you any insight into anyone else’s birthday. Independence can easily be ruined if we are at a gathering of twins or a gathering of people who were born after an historical event. Examples of an historical event that can create a boon in births are something as simple as an electrical blackout that hits a large metropolitan area like New York City. I guess any event that affects people’s normal nighttime activities might lead to a situation where procreative activities are changed. Anyway, our assumptions are that each of the 365 birthdays is equally likely (our data from 1978 does not really support this conclusion) and that the people gathered have unrelated birthdays. I guess you might be able to simulate this experiment by selecting n people at random and then see if anyone in the gathering of these n people has the same birthday. You would have to repeat this many times to get an idea of what is happening.

Here's where I want to create a distributive Internet project from around the world to start sampling this population of data. Now, Go ahead and start sampling, at random, by downloading Worksheet #3 from the sidebar and answer the questions. Submit them to your instructor to see if you've done it right! Your instructor will then submit them to me for tabulation and publication. This may take time.