You have a sack of coins. Each coin can have a different bias. The biases are unknown. You flip each coin. If the coin comes up tails, you remove the coin from the sack. If it's heads, it remains in.
You start with 1,000 coins. 950 are heads and you remove 50. The next flip, 855 are heads, so you remove 95.
The question is how to approach the posterior with Bayes. The first flip seems easy: a binomial with 1,000 flips, so you can use a beta function to get the mean and the standard deviation. What do you do with the second flip? Does removing the tails from the bag mean that the first flip is no longer usable, or can you use the first flip as a prior belief for the second flip? Can you use beta functions for the posterior of the second flip?