Suppose you think Coin 2 is biased and lands heads some unknown fraction r of the time. Your uncertainty about the parameter r will be represented by a probability distribution: say it’s normally distributed with a mean of 0.5 and a standard deviation of 0.1. The point is, the probability of r having a particular value is a different question from the the probability of getting heads on your first toss of Coin 2, which is still 0.5.
A standard approach is to use the beta distribution to represent your uncertainty over the value of r.
A standard approach is to use the beta distribution to represent your uncertainty over the value of r.