总结outline：
- 3 axioms of prob. (第三点证明待补充)
- properties
2.1 commutativity P(A+B) = P(B+A) = P(A)+P(B) - P(AB) 2.2 associativity P(A+B+C) = P{(A+B)+C}
2.3 distributive laws (A+B)*C = (AC)+(BC); (A*B)+C = (A+C)*(B+C)[note: + means union; and * means intersection ]
2.4 inclusion-exclusion: P(A1+A2+A3+…+An) = inclusion of one at a time -/exclusion of two at a time + inclusion of three at a time +….(-1)^(n+1)P(A1A2A3…An)
2.5 Demorgan’s laws: (A+B)^c = A^c * B^c; (A*C)^c = A^c + B^c [union and intersection exchange] - calculations
3.1 conditional prob.
3.2 total prob.
3.3 Bayes’ formula/rule 3.4 indep. events (pairwise indep vs jointly indep) - intro: chapter 1, 19, 25, 27, 32/example 2.5(page 23)/demontmort’s problem, 48.
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