For a binomial experiment, is it possible for the probability of success to change from one trial to the next? I figure that the answer would be no, that as long as the trials are independent (a feature of a binomial experiment, right?), then it would not be possible for the probability of success to change, Am i understanding it correctly?

Yup you get it! (Probability doesn't change, it is constant for all trials)

Step-by-step explanation:

In binomial experiments, you have two conditions, a success and failure is how they often put it. In this experiment, the probability of success has to be the same for each trial to constitute it as a binomial experiment.

Basically there's 4 rule you need to satisfy for an experiment to be considered binomial:

1) Has to have fixed number of trials. Eg, n=1,2,3 ... x x = finite number (we cannot have infinte trials)

2) Each trial is independent of one another. (One trial doesn't influence another trials probability/outcome)

3) Only two outcomes (very important) because as name suggests bi - (bi usually means two)

4) Probability of each outcome/condition is constant from one trial to another

Yes you are understanding correctly