Checkpoint 4.9.5. Shared Birthdays.

In this problem, you want to consider how many people are necessary in order to have an even chance of finding two or more who share a common birthday. Toward that end, assuming a year has exactly 365 equally likely 4.3.11 days let r be the number of people in a sample and consider the following:
  1. Determine the number of different outcomes of birthdays when order matters and birthdays are allowed to be repeated.
  2. Determine the number of different outcomes when birthdays are not allowed to be repeated.
  3. Determine the probability that two or more of your r students have the same birthday.
  4. Prepare a spreadsheet with the probabilities found above from r=2 to r=50. Determine the value of r for which this probability is closest to 0.5.
  5. As best as you can, sample two groups of the size found above and gather birthday information. For each group, determine if there is a shared birthday or not. Compare your results with others in the class to check whether the sampling validates that about half of the samples should have a shared birthday group.
Solution.
in-context