Probability
Independence, conditioning, and the intuitions that lie.
the shape of this subject
Probability problems trick even careful students. Brainback trains you to write the sample space before you count.
Because probability rewards the students who do the reps — and punishes the ones who outsource them.
- discipline
- STEM
- parent subject
- Statistics
- typical weekly load
- 3-6 problem sets · 3-5 hours · 1-2 recall sessions
- covered on plan
- all plans (free forever)
Every probability concept Brainback covers.
Add Probability as a Learn subject and every problem in these areas routes to the Socratic tutor — attempt-first, hint-laddered, output-guarded.
What one turn in probability actually looks like.
Attempt → correction → guiding question. No answer. Ever. Verbatim from a beta session.
I used complement: P(at least one) = 1 − P(none)…
What's P(A|B) in words before you compute it?
no answer · one guiding question · your next move
How real attempts start. How Brainback nudges.
- I used complement: P(at least one) = 1 − P(none)…
- What's P(A|B) in words before you compute it?
the anti-pattern
What probability looks like when the AI does the thinking.
Answer machines make probability look like a solved problem. It isn't. The exam room reveals whose reasoning was built and whose was rented.
- M1Applying a formula without checking whether the conditions actually hold.
- M2Skipping the sanity check — 'does the sign / magnitude make sense?'
- M3Memorizing steps instead of reasoning about why they're legal.
- M4Reading past the setup and diving straight into computation.
the recall card
What a spaced-repetition card looks like in probability.
Every wrong attempt and low-scored explain-back becomes a card. SM-2 schedules them — the tricky ones come back tomorrow, the solid ones drift out to next week, then next month.
Recall the core concept in your own words. Then apply it to a fresh example under 2 minutes.
Related subjects.
The subject where the shortcut has always been most expensive.
Limits, rates, and shapes of change — earned, not delivered.
Where symbolic manipulation becomes second nature — or doesn't.
See the diagram. Not just look at it.
Unit circle, but also unit intuition.
Vectors are directions, not numbers.
probability — ready when you are
Start your first probability session.
Attempt-first. Never the answer. Add it as a Learn subject in 30 seconds.