Probability project

Probability project

1. Concepts

   • Odds: comparition of # favorable outcomes and # of total outcomes
   • Sample space: The set of all possible outcomes
     • Event: subset of sample space
   • Experiment: Any observation measurement of random phenomenom
     • Outcome: possible results of the experiment.

2. Probability formulas

   • Theorical probability: # of favorable outcomes / Total # of outcomes
   • Empirical probability: # of times an event occurred / Total number of outcomes

3. Venn Diagrams

   • Union: A u B
   • Difference: A - B
   • Intersection: A n B
   • Complement: A´

4. Events with "and"

   • Multiplication rule
     • For any two events: P(A and B) = P(A) - P(B)
     • For independent events: P(A and B) = P(A) * P(B)
   • Conditional probability formula
     • Conditional probability of B given A
       • P(A n B) / P(A)

5. Events with "not" or "or"

   • Certain event: P = 1
   • Probability value: 0<P<1
   • Impossible event: P = 0
   • Addition rule
     • If A and B are any two events: P(A or B) = P(A) + P(B) - P(A and B)
     • If they are mutually exclusive: P(A or B) = P(A) + P(B)
       • Mutually exclusive events can not happen at the same time.
   • Probability of complement
     • P(not E) = 1-P: Everything but the event