I will use an example to better illustrate my problem.
Assume that we are given a well furnished room with a dog inside. We know that the dog can either be a friendly dog or an unfriendly dog. Further assume that if we knock the door, a friendly dog and an unfriendly dog will have a different probability to bark. Say a friendly dog will bark with probability 10% and an unfriendly dog will bark with probability 50%.
Now the primary question is how could we run a test by knocking the door to test whether the dog is friendly or unfriendly? What confidence could we obtain with the test? We could knock the door as many times as we want, but for efficiency reasons we may want to make a conclusion with as few knocks as possible.
One step further, what if we only know that an unfriendly dog has a higher probability to bark than a friendly dog but we don't know the exact probability? This will lead to an open question and is there a potential good solution for this scenario too?
Thanks fellows and any discussions will be useful.