Excel result
I had a couple minutes while some coffee was brewing, so I ran this in excel. A couple minutes is all it takes since excel has the function COMBIN for doing combinations. I won't give the result, but I will say that you should not use my suggested approximation as it doesn't give good results. The problem is that when you change the probability from 1/2 to 18/38, the split between <=12 and >=13 is not close to 50-50 anymore, it is about 60-40.
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