1. Basics:

Basic theoretical probability, Randomness, probability, and simulation: Probability , Probability using sample spaces, Multiplication rule for independent events, Counting principle and factorial, Combinatorics and probability, Binomial random variables: Random variables, Sampling distributions, Significance tests (hypothesis testing) , Two-sample inference for the difference between groups.

2. Building an intitution:

Partitions, Multinomial probilities, Bernoulli and indicator random variables, Uniform random variables, Binomial random variables, Conditional PMFs, Hat problem, Inclusion-exclusion formula, Variance of geometric.

3. Probability and Statistics in Data Science using Python:

Random variables, dependence, correlation, regression, PCA, entropy and MDL.