Probability turns our uncertainty about whether an event occurs into numbers: the value means “impossible”, the value “certain”, and everything in between describes uncertainty of varying degree. This chapter presents probability systematically, starting from the basic definitions (event, sample space, partition, Kolmogorov’s axioms) and reaching the most powerful theorems (total probability, Bayes), the equivalent graphical tools (tree diagram, Venn diagram, contingency table) and finally the discrete distributions (the Bernoulli scheme and the binomial distribution), expected value with its applications to betting and game theory, and an appendix on descriptive statistics. The chapter closes with a gallery of classic paradoxes showing how often our intuition, in probability, is misleading.
Sections
- Sample space, events, partition
- Definition of probability
- Mutually exclusive and independent events
- Conditional probability and correlation
- Tree diagram
- Total probability, Bayes and inverting the tree
- Venn diagram and contingency table
- Worked examples with Venn and table
- Diagnostic tests
- Three equivalent representations
- Combinatorics and probability
- Binomial distribution
- Expected value and fair games
- Games of chance for one player
- Two-player games
- Descriptive statistics and surveys