500
The mathematical formulation for the expected value of the bias of a coin p given the coin has an initially unknown bias and has been flipped 3 times with the result {H, H, T}.
What is
Integral( p * ( (3c2)*(p^2)*(1-p) / Integral( (3c2)(p^2)(1-p) dp )[0, 1] ) dp)[0, 1]