Probability

Probability

1. Odds

   • compare the number of favorable outcomes to the number of unfavorable outcomes

2. probability formulas

   • Theoretical Probability Formula
     • P(E)=Number of favorable outcomes/Total number of outcomes
   • Empirical Probability Formula
     • P(E)=number of times event E occurred/number of times the experiment was performed

3. Basic concepts

   • Outcomes
     • Possible effects obtained from an experiment
   • Sample espace
     • set of all possible results
   • Event
     • Sub-set of the sample space
   • Experiments
     • Random phenomenal

4. Events involving "not" and "or"

   • Properties of Probability
     • Probability value
       • A number from 0 throught 1
     • Impossible Event
       • If E is imposible then n(E) must be 0 P(E)=0
     • Certain event
       • Dividing the members of the inequality by n(s) so it gives you 0<n(E)<n(s)
   • Porbability of the complement
     • The probability that an event E will not occur is equal to one minus the probability that it will occur P(not E)=1-P(E)
   • Addition rule of probability
     • If A and B are any two events, then P(A or B)= P(A) + P(B) - P(A and B)
     • If A and B are mutually exclusive, then P( A or B)= P(A) + P(B)
       • Two events are mutually exclusive events if they have no outcomes in common

5. Events involving "and"

   • Conditional probability
     • The probability of event B computed on the assumption that event A has happened is called the conditional probability of B given A and is denoted P (B|A)
     • Formula
       • P( A n B)/P(A)= P(A and B)/ P(A)
   • Multipication rule of probability
     • For any 2 events
       • P(A and B)=P(A)xP(B/A)
     • For independent events
       • P(A and B)= P(A)x P(B)

6. Venn diagrams

   • Set operations
     • Complement
       • A'=(x|x E u and x E A)
     • Intersection
       • B(x|x E A or x E B)
     • Difference
       • A-b={x|x EA and x º\ B)
     • Union
       • A u B= {x|x EA or x EB}