TOPIC 2.docx - TOPIC 2 \u2013 PROBABILITY I Definition Probability P(A is the probability of an event A occurring Sample space S is the set of all possible

TOPIC 2.docx - TOPIC 2 – PROBABILITY I Definition...

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TOPIC 2 – PROBABILITY I. Definition - Probability : P(A) is the probability of an event A occurring - Sample space : S is the set of all possible outcomes and have to cover everything - Complex : is made of elementary events and doesn’t have to be made of everything - Event : A is an event made up of a subset of outcomes f rom the sample space - Outcome : C i is the value of a specific outcome i, i ϵ (1, .., N) II. Set Theory - Union : A B is the set of all elements which are in A or B or both (Or) - Intersection : A ∩ B is the set of all elements which are in both A and B (And -> find the common, if given graph, don’t do P(A) P(B), just find the common between 2) - Complement : A c is the set of all elements which are not in A (Nor) => P(A) = 1 – P(A c ) - Mutually exclusive and exorcist => Neither nor: P (A but not B) = P(A) - P(both) = P(A) - P(B) P(A|B) Example: When roll a six-sided dice. C 1 C2 C3 C 4 C5 C6 S = {1,2,3,4,5,6} => Elementary events Complex events (made of elementary events)
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A = {2,4,6} B = {1,2,3} a. What is (A∩B) -> and - A∩B: Elements that are in common of A and B, which is 2 => (A∩B) = {2} => Use multiplies b. What is (A ∪B) -> or - A ∪B: Elements that are in both A and B => (A B) = {1,2,3,4,5,6} => Use adds III. Set rules 1. A B = B A 2. A ∩ B = B ∩ A 3. A (B C) = (A B) C 4. A ∩ (B ∩ C) = (A ∩ B) ∩ C 5. A ∩ = 6. A = A 7. (A c ) c = A 8. A (B ∩ C) = (A B) ∩ (A C) 9. A ∩ (B C) = (A ∩ B) (A ∩ C) 10. (A B) c = A c ∩ B c 11. (A ∩ B) c = A c B c IV. Classical (theoretical) probability Probability of event happening = Number of favorableoutcomes Number of possibleoutcomes Example 1: What is P (A∩B) => P (A∩B) is the element that is in common of both A and B, which is 2 => P (A∩B) = General multiply rule P (A∩B) = P(A) P(B|A) +) P(A) = Number of outcomes A Number of sideof thedie = 3 6 3 number in A 1 number in A and B
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+) P(B|A) = Number of outcomes both B A Number of outcome B = 1 3 => P (A∩B) = 3 6 x 1 3 = 1 6 Specific multiply rule + Multiply rule: P (A∩B) = P(A) P(B)
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  • Spring '14
  • Schmid
  • Probability theory,  P

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