Probability

Probability asks a different question than Statistics does: given a known model — a fair coin, a standard deck of cards, a six-sided die — what's the chance of a particular outcome? Statistics works in the opposite direction, starting from real data and trying to infer what's going on. That distinction matters for a student because the two subjects, while related, use different tools.

Probability leans on combinatorics: counting how many ways an event can happen, using permutations when order matters and combinations when it doesn't, then building toward compound events, conditional probability, and independence — whether one event happening changes the odds of another.

Two ideas tend to trip students up specifically. The first is the difference between "or" and "and" in probability language — adding probabilities for one event or another versus multiplying them for both happening together — which sounds simple stated abstractly but gets genuinely confusing once conditions and dependencies are layered in.

The second is conditional probability itself, particularly problems involving Bayes' theorem, where the intuitive answer and the correct answer often diverge (the classic example being a medical test with a low false-positive rate that still produces mostly false positives when the underlying condition is rare). Probability distributions — binomial, and for more advanced courses, normal — round out the material, connecting counting problems to the bell-curve concepts a student may already have encountered informally.

A tutor can work through this at whatever level a specific course requires, from basic counting rules through distribution problems.