Unit 2 of 2

Counting and Probability

Nine lessons. The unit where you stop enumerating and start reasoning. Linearity of expectation lets you compute an expected value without ever knowing the distribution, which feels illegal the first few times you use it. Complementary counting turns brutal problems into easy ones by asking the opposite question. And recursion quietly reveals that half the counting problems on the AMC are Fibonacci wearing a costume: no two adjacent, domino tilings, climbing stairs, frogs jumping, ten women reseating themselves. Same recursion, five disguises. Covers permutations and combinations, casework, inclusion and exclusion, stars and bars, binomial identities, probability, expected value, geometric probability, and state machines.