I was amazed recently when I learned of this figure I am about to explain to you.

Coin flipping probability is quite simple, but it is also quite interesting when you actually look at the figures. A boring and intuitive thing to say is that with a fair coin (i.e. not biased to either heads or tails due to weighting the coin or something else) if it is flipped many times, the percentage of heads recieved would approach 50%.

The interesting fact that brings us to this node today is the probability of getting either 25 or 75 heads in 100 tries. I will give you the answer first and then I will explain it. The answer is one in 5.2 million. If you do 100 flips 5.2 million times you might get one instance where you recieve either 25 or 75 heads.

Investigating this figure, one notices that the function of the number of flips and the results (# of heads) forms a rather steep bell curve. The peak of the curve is at 50 for 100 throws. As you approach either 25 or 75 heads, the probability gets shockingly low. To be precise, one in 5.2 million.

     |           *
     |          * *
     |          * *
  #  |          * *
 of  |         *   *
flips|         *   *
     |        *     *
     |       *       *
     |     *           *
     |*****             *****
    0            50
              # of heads
You can see that as (# of flips) approaches infinity, (# of heads) centers right around 50%. Pretty cool, right?

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