Today is used to evaluate the students understanding of both modeling and expected value. Any number of questions similar to those earlier in the week can be used to pinpoint strengths and weaknesses, but the culminating activity should be done in groups.
If you were to randomly ask people what their birthday was, how many people would you expect to ask before you duplicated a birthday (this can also be done as the birthmonth). Do not expect them to come up with an analytical solution to this problem... it is very long and messy (the birthmonth problem might be manageable, though).
Allow them to use any tools (coins, cards, dice, computers, etc.) to create a model and find an answer. Development and description of the model should be the most important part of the project.
NOTE: The downloaded Hermit Problem program (for Macs) can be used to model this problem by setting the #Hermits to CUSTOM and choosing 365 (each hermit represents a day of the year--February 29th not included). The program will run until one of the hermits (birthdays) is visited twice (is duplicated). Pretty sneaky, huh?
If you like, you may return to the introduction page.