The Nature of Probability

• An experiment is a controlled operation that yields a set of results.
• The results of an experiment are called outcomes
• An event is a set of outcomes of an experiment.

• An experiment is rolling a six sided die
  The outcomes of this experiment are 1,2,3,4,5,6 show on the top face
  An Event is that an even number shows on the top face
        

• An experiment is a fair coin is tossed
  The outcomes of this experiment are heads or tails show on the top side
  An event is that the heads side is showing.
        

  An experiment is drawing a single card from a deck of cards
  The outcomes are (not going to list them here)
  An event is that the card is black.
        

• Empirical probability involves conducting experiments and observing the outcomes.
• Theoretical probability involves studying the experiment and outcomes without conducting the events.
• For empirical probability

          The number of times an outcome favorable to E occurred
  P(E) = -------------------------------------------------------
          The total number of times the experiment was conducted
        

• Do selected odd problems, page 729
• The law of large numbers states that probability statements apply to a large number of trials, not a single trial. The relative frequency of events is predictable in the long run, not for individual events.

Theoretical Probability

• If all of the outcomes of an experiment have the same chance of occurring, the we say that all outcomes are equally likely

          The number outcomes favorable to E occurred
  P(E) = ----------------------------------------------
             The total number of possible outcomes
        

• If an event E cannot occur, P(E) = 0, if P(E) = 0, then E cannot occur
• If an event E must occur, P(E) = 1, if P(E) = 1, then E must occur.
• For any event E, 0 ≤ P(E) ≤ 1
• For an event A, P(A) + P(not A) = 1
• Do questions 13 to 77, your choice.