Before decrypting the solution: What do you mean by "be fully certain of being p certain of"? It is entirely sensible to create a Bayesian agent that is fully certain about its probabilities by construction. And even if it isn't, the goal as you put it was to be p-certain of having achieved the goal, not to be absolutely certain of being p-certain of having achieved the goal. I am even not sure how would the recursive probabilities of probabilites be supposed to work.

Edit after decryption: well, ok.