Having a class for this is really overkill, and makes the code hard to understand.

It looks to me like the state you need to keep track of is:
 * whether you're in practice mode
 * how many times the user has flunked practice mode
 * a list of trials for the current phase of the test (e.g. practice or the real thing)
 * the current index in that list

And then you need a function that can generate a randomly shuffled list of trials, possibly repeated.

(As an aside, does EXAMINER really repeat the exact same sequence of trials twice?)