Simulating Probabilities

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1) Design a simulation for the classic birthday problem to determine how likely it is that at least two people in a class of 30 share a birthday. (If you want an extra challenge, calculate  the theoretical probability is and compare.)

2) Imagine that students arrive one at a time into the classroom. Determine how many students, on average, you need to see to have two with the same birthday.

The simulation for (2) is somewhat tedious, unless you're a good programmer. So do 5 repetitions and post your results on the discussion board. Incorporate the others' posted results into your own milestone report. Name your file ms08yourlastname and drop in the Drop Box. Your discussion should make it clear what constitutes a "trial" in each simulation. For the first simulation, you should also explain how many times (N) you repeat the trials to arrive at your estimated probability and why you are comfortable with that number, if in fact you are.