Bayes Biliard¶
\[\int_0^1 \binom{n}{k} x^k (1-x)^{n-k} dx = \frac{1}{n+1}, 0 \le k \le n\]
We start with N balls we throw them, than we pic one at random and paint it grey. The probability that we pick one particular ball is \(\frac{1}{n+1}\)
We start with N balls we throw them, than we pic one at random and paint it grey. The probability that we pick one particular ball is \(\frac{1}{n+1}\)