Probability Theory · 41 lessons

Probability is the one branch of school mathematics where a correct calculation regularly contradicts a strong intuition — and where the intuition is usually the thing that is wrong. The arithmetic is easy; the difficulty is always in stating precisely what event you are asking about.

1. 1The Probability Scale
2. 2Sample Space
3. 3Single-Event Probability
4. 4Complementary Events
5. 5Experimental Probability
6. 6The Law of Large Numbers
7. 7Expected Counts from a Chance
8. Logic and counting (11)
9. Chance (11)
10. 8Naming the Regions of a Venn Diagram
11. 9Possibility Diagrams
12. 10Chance from Areas
13. 11Mutually Exclusive Events
14. 12The Addition Rule for Overlapping Events
15. 13Independent Events
16. 14Tree Diagrams
17. 15The Chance of At Least One
18. 16Without Replacement
19. 17Multiplying Along a Tree Without Replacement
20. 18Conditional Probability
21. 19Conditional Probability Notation
22. 20The Monty Hall Problem
23. 21The Birthday Paradox
24. 22Why a Positive Test Can Still Mean Healthy
25. 23Reversing a Tree: the Base-Rate Answer
26. Probability with Several Events (12)
27. 24Probability in Set Notation
28. 25Conditional Probability from Tables
29. 26Random Variables
30. 27Probability Distributions
31. 28Expected Value
32. 29Variance
33. 30Transforming a Random Variable
34. 31Bernoulli Trials
35. 32The Binomial Distribution
36. 33Binomial Mean and Variance
37. 34Modeling with a Binomial
38. 35Continuous Variables
39. 36The Normal Distribution
40. 37Standardizing
41. 38Reading the Z-Table
42. 39Reading Normal Probabilities
43. 40Inverse Normal
44. 41Combining Normals
45. Probability Distributions (10)