It's true that individual actions are very random, but I think Bitty is right about the larger data having average closer to the chance.
You can try this out in a spreadsheet. Add a small amount of random numbers between 0-1. The average is probably not very close to 0.5 (the middle point). Now start adding more random numbers and you will see the average getting closer to 0.5 more often.
So I think you can calculate the chance if you have enough data. What is enough data? Depends on the chance, if the chance is smaller you need more data.
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I don't want to be the oneThe battles always choose
'Cause inside I realize
That I'm the one confused