# Frequentist approach to marginalize nuisance parameters

How would be a frequentistic approach to solve this problem?

"We have a random machine that gives 0 or 1 with a hard-coded, fixed but unknown probability $$p$$. After 10 trials we have 5 "0" and 5 "1". Which is the probability to have a "0" and a "1" in the next two trials?"

I know how to approach the problem with Bayesian inference and marginalizing the nuisance parameter $$p$$, but how problems like these can be answered in frequentistic way? It is even making sense as a question from a frequentistic standpoint?

I saw similar problems giving confidence intervals for $$p$$ given an initil set of trials, but how to use that to give probabilities on following trail outcomes?