Chapter 12, section 1 and 2.

The Nature of Probability

• An experiment is a controlled operation that yields a set of results.
• The results of the experiment are called outcomes
• An event is a subset of the outcomes of the experiment.
• An experiment can be flipping a coin, tossing a 6 sided die or drawing a card from a standard deck of cards.
• Empirical Probability is determined by conducting the experiment a number of times, and counting the number of times the event occurs.
• P(E) = number of times E occurred / number of experiments.
• The Law of Large Numbers states that probability statements apply in practice to a large number of trials, not a single trial. It is the frequency over the long run that is accurately predictable, not individual events.
• Example problems:
  • Discuss 12, p 729
  • 15
  • 18
  • 22
  • 24
  • 26

Theoretical Probability

• The Theoretical Probability of an event E is determined by studying the possible outcomes that can occur.
• P(E) = Number of outcomes favorable to E / Total number of outcomes.
• We either deal with equally likely outcomes or we weight the outcomes to be equally likely.
• Find the probability that a 2 shows when a 6 sided die is tossed.
• Find the probability that an even number shows when a 6 sided die is tossed.
• If an event cannot occur, the probability is 0
• Find the probability that a 7 shows when a 6 sided die is tossed.
• If an event must occur, the probability of that event is 1
• Find the probability that a number less than 10 shows when a six sided die is tossed.
• The probability of an event is E, 0 ≤ P(E) ≤ 1
• The sum of all of the probabilities of all of the possible outcomes of an experiment is 1.
• P(A) + P(not A) = 1
• P(a_ = 1 - P(not A)
• Do problems 13, 17-26, 27, 28 31-34,