Probability

Probability

1. BASIC CONCEPTS

   • EXPERIMENT: Any observation measurement of random phenomenon
     • OUTCOMES: Possible results of the experiment
       • SAMPLE SPACE: Set of all possible outcomes
         • EVENT: Subset of sample space
   • ODDS: Comparison between the number of favorable outcomes to the number of unfavorable outcomes

2. FORMULAS

   • THEORICAL
     • P(E) = # of favorable outcomes / Total Outcomes
   • EMPIRICAL
     • P(E) = # of times an event occurred / Total outcomes

3. EVENTS INVOLVING: AND

   • MULTIPLICATION RULE OF PROBABILITY
     • For any 2 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, means: P (A n B) / P (A)

4. VENN DIAGRAMS

   • UNION (u): Bot A and B
   • DIFFERENCE (-): A without B
   • INTERSECTION (n): Part shared by A and B
   • COMPLEMENT (´): Everything in the universe but the letter with the complement

5. EVENTS INVOLVING: NOT / OR

   • FORMULAS
     • Certain event: Probability = 1
     • Impossible event: Probability = 0
     • Probability value; Probability is more that 0 but less than 1
   • ADDITION RULE
     • A and B are any two events: P (A or B) = P(A) + P(B) - P(A and B)
     • Mutually exclusive: P (A or B) = P(A) + P(B). Can´t happen at the same time mutually exclusive.
   • PROBABILITY OF COMPLEMENT
     • P (not E) = 1 - P(E)