> we can conclude that the coin is weighted in some way with P=0.03125 No we can't. There are 2 (related) reasons for this. The first is that to say "after e

> we can conclude that the coin is weighted in some way with P=0.03125 No we can't. There are 2 (related) reasons for this. The first is that to say "after experiment X, we can conclude thing Y is happening with probability ..." you need to know something about how often thing Y happens on its own. This is also known as a prior. The other reason is that in this specific case, the prior for Y (that the coin is weighted) can be concisely summarized as P(Y)=0, because it's physically impossible to construct a coin that's biased to one side or the other (independent of what side it starts on). Some people think the coin flipping examples are bad because biased coins are impossible, but they're actually good for exactly this reason. We have a really good prior (from math/physics/geometry) that biased coins can't exist, so you're going to have to not only flip a lot of them to convince me otherwise, but also give me an explanation of how that's possible (i.e justify your prior)