The document introduces basic probability concepts and provides examples to illustrate them. It discusses the key properties of probability, types of probability (objective and subjective), mutually exclusive and collectively exhaustive events, and probabilities of independent and dependent events. It also explains Bayes' theorem and how it can be used to update probabilities as new information becomes available.

1. Probability Concepts and Applications

15. P(A and B) (Venn Diagram) P(A) P(B) P(A and B)

16. P(A or B) + - = P(A) P(B) P(A and B) P(A or B)

19. Probability(A|B) Independent Events P(B) P(A) P(A|B) P(B|A)

23. Probability(A|B) / P(A|B) = P(AB)/P(B) P(AB) P(B) P(A)

24. Probability(B|A) P(B|A) = P(AB)/P(A) / P(AB) P(B) P(A)

30. General Form of Bayes’ Theorem

36. Further Probability Revisions - continued