2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC Examples 0 play a dice--2={1,2,3,4,5,6} event A={point is 1}={1} event B=frolling an odd number}={1,3,5} event C={point is more than 4}={5.6} 4日·5.421手，300C0 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES Examples 1 play a dice))Ω = {1, 2, 3, 4, 5, 6} 2 event A={point is 1}={1} 3 event B={rolling an odd number}={1,3,5} 4 event C={point is more than 4}={5,6} Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO 4.elementary set operations 1.implication If AC B,the occurrence of A necessarily implies the occurrence of B (or equivalently.BCA) Eg.:140 years old}c{30 years old} for any A,we have cAC O 2.equality:ifA C B and B C A,we say that A and B are equal and write A=B O 3,Union:the union of A and B,written AU B,is the set of elements that belong to either A or B or both U21A,UA Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 4!elementary set operations 1 1!implication :If A ⊂ Bßthe occurrence of A necessarily implies the occurrence of B£or equivalently. B ⊂ A§ Eg.µ{40 years old}⊂{30 years old} for any Aßwe have φ ⊂ A ⊂ Ω 2 2!equality :ifA ⊂ B and B ⊂ Aßwe say that A and B are equal and write A=B 3 3!Unionµthe union of A and B,written A ∪ B, is the set of elements that belong to either A or B or both ∪ n i=1Aiß∪∞ i=1Ai Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCC 4.elementary set operations 1.implication If AC B,the occurrence of A necessarily implies the occurrence of B (or equivalently.B CA) Eg.:140 years old}c30 years old} for any A,we have Ac 2.equality ifA C B and BCA,we say that A and B are equal and write A=B 3.Union:the union of A and B.written AU B.is the set of elements that belong to either A or B or both U1A·UA 4口·5,4，手·3900 Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 4!elementary set operations 1 1!implication :If A ⊂ Bßthe occurrence of A necessarily implies the occurrence of B£or equivalently. B ⊂ A§ Eg.µ{40 years old}⊂{30 years old} for any Aßwe have φ ⊂ A ⊂ Ω 2 2!equality :ifA ⊂ B and B ⊂ Aßwe say that A and B are equal and write A=B 3 3!Unionµthe union of A and B,written A ∪ B, is the set of elements that belong to either A or B or both ∪ n i=1Aiß∪∞ i=1Ai Xiaohan Yang Chapter 2 Axioms of Probability
2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCO 4.elementary set operations 1.implication If AC B,the occurrence of A necessarily implies the occurrence of B (or equivalently.BCA) Eg.:140 years old}c30 years old} for any A,we have Ac 2.equality:ifA C B and BC A,we say that A and B are equal and write A=B 3.Union:the union of A and B,written AU B,is the set of elements that belong to either A or B or both UR1Ai,UR1Ai Xiaohan Yang Chapter 2 Axioms of Probability
logo 2.2 SAMPLE SPACE AND EVENTS 2.3 AXIOMS OF PROBABILITY 2.4 SOME SIMPLE PROPOSITIONS 2.5 SAMPLE SPACES HAVING EQUALLY LIKELY OUTCOMES 4!elementary set operations 1 1!implication :If A ⊂ Bßthe occurrence of A necessarily implies the occurrence of B£or equivalently. B ⊂ A§ Eg.µ{40 years old}⊂{30 years old} for any Aßwe have φ ⊂ A ⊂ Ω 2 2!equality :ifA ⊂ B and B ⊂ Aßwe say that A and B are equal and write A=B 3 3!Unionµthe union of A and B,written A ∪ B, is the set of elements that belong to either A or B or both ∪ n i=1Aiß∪∞ i=1Ai Xiaohan Yang Chapter 2 Axioms of Probability