Each learning path is one chapter: a guided route through a topic, one small course at a time. Pick a class to see its chapters in order.
A friend peeks at your card and says it is a heart. Your chances change at once. A test says a patient is ill, and still the patient is probably healthy. Both surprises come from the same idea: new information changes a probability. This chapter shows how to update a probability with conditional probability, how to chain events with tree diagrams, how to turn a result around with Bayes' theorem, and how to describe a repeated trial with a random variable and the binomial distribution. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python checks every probability in exact fractions.