Birthday problem

There are 23 people at a party. How likely is it that at least two of the 23 people have the same birthday? To simplify, ignore lap years, and assume that all days are equally likely to be birthdays. We argued in class that the answer is .5072

An alternative way to get the probability in question is using the limiting frequency idea. To do this you can use computer simulation to generate a number of different parties, and then count how many of the simulated parties include at least two people with the same birthday. In Unix Minitab

random 23 c1-c20; 
integers 1 365.

will generate 20 parties of 23 people each with equally likely birthdays. Each party is stored in a column. Then use

tally c1-c20

to display the results. How many of your 20 sets of 23 birthdays had no matching birthdays? What is the estimate of the probability of interest based on the simulation?

Note. Please do not to hand in the entire tally. Just give a brief summary of the results.