Finite Probability and its Applications Final Notes

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Course Code
MATH 1004
Ellen Julia Goldstein

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Finite Notes Set is any collection of objects Elements are objects in the set Union of Sets= A U B (Anything that belongs to A, B, or both) Intersection of Sets=A ∩B  (anything that belongs to both A and B) Subset:  The set B is a subset of the set AB∩ Aitte, every element in B is also an element of A Compliment: À of a set is the set of everything that does not belong in set A Inclusion­ Exclusion Principle: n(S U T) = n(S) + n(T)—n(S    T) Special Case: if S   T don’t equal 0: n(S U T)=n(S) + n(T) De Morgans Laws: (S U T)’=  S'∩T' and  (S∩T)' = S’ U T’ Multiplication Principle: Task has two consecutive choices. Choice 1 can be performed in m ways and,  for each of these, choice 2 can be performed in n ways…complete task can be done in mn ways Permutations: P(n,r)=n(n­1)(n­2)…(n­r+1)  ▯r factors n! Combinations: C(n,r)= r!(n−r)! Binomial Theorem: Expand (x+y) n n n k n−k (x+a)= ∑ () x a k=0 k A set of n elements has 2   subsets Logical Probability: obtained by mathematical reasoning Empirical Probability: obtained by sampling or observation and is calculated as a relative frequency Judgemental Probability: Educated Guess Addition Principle: Pr(E)= Pr(s)+Pr(t)+Pr(u)+…+ Pr(z) a Converting between odds and probabilities:r(E)= (a+b) Numberof outcomes∈E Pr (E)=  N Complement Rule: Pr(E)= 1­Pr(E’) (number of outcomes∈E∩F) Pr( E∩ F)=  (number of possibleoutcomes) Conditional Probability: r(EΙ F)= numberof outcomes∈E∩F numberof outcomes∈F Product Rule: If Pr(F)≠  0:  PrE∩F=Pr⁡(F)×Pr⁡(E Ι F) Independent Events:  Pr(E∩F)=Pr(E)∙Pr(F) Nonzero Proba
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