What I've Done With My Physics Degree Part 3: You're Unique and Special, Just Like Everyone Else

Everyone has those vivid memories of ordinary experiences.  For no reason whatsoever, I can distinctly remember being 4 years old and watching an episode of the Flintstones with my grandma.  It wasn't an unusual experience, or a traumatic one, watching cartoons was part of my routine as a toddler.  Yet, for some reason or another, I remember this episode almost two decades later.  The plot opened up with the narrator commenting about how it is commonly believed that everyone in the world has their own twin
No, not identical twins.  They were talking about two unrelated people from two separate mothers and fathers who happened to look exactly a like.  In the episode, Fred's twin shows up in Bedrock and causes trouble as people think Fred's doppleganger is really Fred.

Now, years later, I am trying to think of the math behind this episode.  Is it really possible that some other person born from different parents has, by sheer probability, the same genetic code??  In principle it's possible.  Once the earth's population is large enough, the probability of someone having the same sequence of DNA will be statistically significant.
Everyone knows that the nucleotides in DNA are made up of four different bases (A, T, C, G)  These bases pair with eachother with in selective ways: A only bonds to T, C only bonds to G and vice versa.  Now again I admit that this is not the entire picture as there is a base U and the base pairings are not always 100% accurate.  However, let's ignore this for the time being...

So there are 3.1 billion nucleotide bases in the human genome.  At first glance, (1/4)^3.1 billion would be the probability of having the same genome as someone else.  Pretty much next to nothing

HOWEVER, all human DNA is pretty much the same in everyone.  In fact, we share over 80% of our genome with a banana.  Scientists have only identified 1.4 million locations where single bases differ (SNPs) in humans.
That means there are only 1.4 million spots that make us unique.  So the new probability is (1/4)^(1.4*10^6).   Which is two hundred orders of magnitude less than a googol.

So basically, the Flintstones was wrong and I just confirmed what I found out in January on facebook during doppleganger week.  I have no twin: celebrity, or otherwise.