I have a database of approximately 55,000 instances. Each of the instances has 3 possible outcomes - A, B and C. These aren't exact figures but about 49% of the instances are A, 48% are B and 3% are C.

I have created a number of theories that attempt to explain when you'd be more likely to expect to see B's, for instance. One theory in particular isolates 610 instances where A shows up 63% of the time, B's show up 33% of the time and 4% are C.

I'm not sure how best to determine a) the degree of confidence I should have that theory has indeed isolated A's at a higher rate than random and that I'm not just looking at noise and b) what degree of confidence I can have that this higher rate of A's will continue into the future.

I'm sure these are basic confidence interval questions for many of you but I'm new to this world so any help is appreciated. Thanks.