An Avianna lab prototype · Track 1: Probability
Master probability through short sessions, adaptive feedback, visual intuition, and hard problems that reveal exactly what kind of hard they are. Not a textbook, not a school course — a training arena.
Open LeetMath for 20–30 minutes and leave with one of four things: a concept became intuitive, a known weakness was diagnosed, a problem-solving move became reusable, or a hard problem became less mysterious. Adults don’t need math made shallow. They need math made legible, compressed, recoverable, emotionally safe, and hard in the right order.
40 original problems from Easy to Boss, each with a solution autopsy and a transfer variant. Tags are hidden until you commit, so the wording can’t cue the method.
Wrong answers trigger specific feedback: the tempting wrong path, what assumption failed, and the repair drill that fixes it. Errors are diagnostic signals, not failure.
Hints preserve learning: first the diagnostic question, then the named move, and only then the solution. Never a jump from confusion to answer.
Every attempt schedules a spaced review. Clean solves wait a week; misses come back tomorrow. The goal is recognizing the idea later, when the surface changes.
Most platforms tag problems by topic and a difficulty number. LeetMath tags every problem by why it is hard — and each hardness dimension comes with the diagnostic question that dissolves it.
Sample-space
Are you counting favorable and total in the same representation?
Conditioning
What exactly became known, and how did it become known?
Dependence
If one event happens, does it change the probability of the other?
Symmetry
Is there an exchangeability hidden under the wording?
Linearity of expectation
Can I count expected local successes instead of the global distribution?
Recursion
After the first move, what smaller version of the problem remains?
Invariant / martingale
What quantity has no drift from one step to the next?
Bounding
What failure event can I union-bound, dominate, or concentrate?
Existence
If I choose randomly, is the expected number of defects less than one?
Representation
What is this problem secretly isomorphic to?
Adversarial wording
What assumption did the wording tempt me to make?
Proof control
Which statement would a skeptical grader reject?
Probability touches adult reality: hiring uncertainty, investing and downside risk, A/B tests, reliability and outages, medical base rates, games and adversaries, AI evaluation under noise. And it has the right elite arc — from counting and conditioning up to random walks, concentration, coupling, entropy, and the probabilistic method. Your real-world intuition is the raw material; the track converts it into formal reasoning.
In this prototype the arena, hint ladders, miss diagnosis, and spaced review are live. Lessons, visual models, and the diagnostic are on the roadmap.