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

Finding the probability that Pascal will be ahead 9 to 6 amounts to finding the probability
that, in 5 flips of the coin, Pascal will win exactly 4 times. This is given by
 total possible outcomes of 5 coin flips Now, the number of ways you can choose r objects from five objects, for different r, is given by the 6th row of Pascal's triangle, which is
Thus the total number of outcomes is 1+5+10+10+5+1 = 32. And, 5C4 = 5. So the probability that Pascal will be ahead 9 to 6 is 5/32 = 0.15625. That is, we expect that this will happen 15.625 percent of the time.
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