Using Wolfram Cloud to look at the Birthday Problem on Mars

In this video we use Wolfram Cloud to look at the classic "Birthday Problem" often considered in introductory probability courses - for a given class size what is the probability that two classmates share a birthday. The probability as a function of class size has an "S Shape". The probability starts off small, builds up, but then saturates. We see that the classic logistic function does not fit the data well (other than both being S-shaped). On the other hand, the data is well fit by: 1 - Exp( b (x-xo)^2) -- sort of a half, upside Bell curve. Next we look at the problem on other planets, namely Mars and Jupiter having 668 and 10476 "days" in a "year" respectively. We find that the fit parameter b is approximately 0.52/"number of days in year'. Within Wolfram/Mathematica we use: Factorial, Table, ListPlot, Plot, FindFit, Values, Show as well as N[ ] to get the numerical value and D[ ] to take the derivative.

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www1.lasalle.edu/~blum/c152wks/Wolfram_Birthday_Mars.pdf