Module 1

Module 1

1. Probability

   • Basic Concepts
     • Outcomes
       • Effects of an experiment
     • Sample Space
       • All the possible results
     • Event
       • Subset of sample space
     • Experiments
       • Random phenomenon
   • Odds
     • a to b (a favorables in E and b against in E)
   • Formulas
     • Teoretical Probability
       • [n(E)]/[n(S)]
     • Empirical Probability
       • n(event happened) ---------------------------- n(experiment was done

2. Events involving "not" and "or"

   • Properties of probability
     • Possible event
       • P(Ø)=0
     • Certain event
       • P(S)=1
     • Probability value
       • 0≤P(E)≤1
   • Probability of the compliment
     • 1-P(E)=P(E')
   • Addition rule of probability
     • P(AUB)=P(A)+P(B)-P(A∩B)
       • Oa Ob

3. Events involving "and"

   • Multiplication rule of probability
     • For any two events
       • P(AyB)=P(A)*P(B/A)
     • For independent events
       • P(AyB)=P(A)*P(B)
   • Conditional probability formula
     • P(A∩B) -------- P(A)
       • Probability of B given

4. Set operations

   • Complement
     • A'={x|x in U and x not in A}
   • Intersection
     • A∩B={x|x in A and x in B)
   • Difference
     • A-B={x|x in A and x not in B
   • Union
     • AUB={x|x in A or x in B

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