Section 13.1: Introduction to Probability

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13.1 Outline

  1. Terminology
    1. experiment
    2. sample space
    3. event
      1. definition
      2. impossible event
      3. simple event
      4. mutually exclusive
    4. die
      1. equally likely outcomes
      2. sample space
  2. Probability
    1. probabilistic model
    2. relative frequency
    3. types of
      1. empirical probabilities (a posteriori)
      2. theoretical probabilities (a priori)
      3. subjective probabilities
    4. law of large numbers
    5. definition
    6. sample space for a pair of dice
    7. finding probabilities by counting
  3. Probabilities of unions and intersections

 

13.1 Essential Ideas

If an experiment can result in any of n mutually exclusive and equally likely outcomes, and if s of those outcomes are considered favorable, then the probability of an event E, denoted by P (E ), is P(E ) =s/n.

Procedure for finding probability by counting:

  1. Describe and identify the sample space, S.  The number of elements in S is n.
  2. Count the number of occurrences that satisfy the event of concern; this is the number of successes, s.
  3. Compute the probability of the event using the formula P (E ) =s/n.