Table of Contents:
The Bridges of Konigsberg
The Value of Pi
Prime Numbers
Famous Paradoxes
The Problem of Points Proof of the Pythagorean Theorem

The logic displayed on the previous two pages may seem simple, but Pascal and Fermat
had therein grasped a very important concept that, though intuitive to us, was revolutionary
in 1654. This was the idea of equally probable outcomes. They realized that the 'probability'
of something happening could be computed by enumerating the number of equally likely ways it could
occur, and dividing this by the total number of possible outcomes of the given situation. This is
what Fermat did when he figured out the 16 different (equally likely) results of tossing a coin 4
times, and then counted the ones which would result in a win for him. Again, this may seem obvious
to you, but many great mathematicians of the 15th and 16th century gave 'solutions' to the problem
of points that were just plain wrong. Something along these lines has happened in the last twenty
years with the Monty Hall Problem.
Problems:
Problem 1Suppose Pascal had been winning 9 to 6 when they he and Fermat were interrupted. How should the 100 Francs be divided?
Problem 2Suppose you had come upon them earlier and noticed that they were tied 5 to 5. You leave and come back 5 flips of the coin later. What's the probability of Pascal being ahead 9 to 6?
to Pascal's Generalization 
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