CHAPTER 3 PROBABILITY 3.1 Basic Concepts of Probability

I. PROBABILITY EXPERIMENTS  Probability is the foundation of inferential statistics.  Probability Experiment: an action, or trial, through which specific results are obtained  Outcome: the result of a single trial in a probability experiment

MORE DEFINITIONS  Sample Space: the set of all possible outcomes  Event: one or more outcomes; is a subset of the sample space  Tree Diagram: one way to list outcomes for actions occurring in a sequence  Simple Event: an event that consists of a single outcome

EXAMPLES Pg 118 Example 1 Pg 119 Example 2

II. TYPES OF PROBABILITY  P(E)= the probability of event E  Classical Probability: (theoretical) used when each outcome is equally likely to occur P(E) = # of outcomes in E total # of outcomes  Pg 120 Example 3

EMPIRICAL PROBABILITY  Empirical Probability can be used when each outcome is not equally likely to occur; also called statistical or experimental probability.  P(E)= frequency of event E = f total frequency n  Page 121 Example 4

LAW OF LARGE NUMBERS  The law of large numbers states as an experiment is repeated over and over, the empirical probability of an event approaches the theoretical probability of the event  Page 122 Example 5

SUBJECTIVE PROBABILITY  Is a result of intuition, educated guesses or estimates.  Page 123 Example 6

RANGE OF PROBABILITIES RULE  Probability can NOT ne negative or greater than 1.  0 ≤ P(E) ≤ 1  0 means it is impossible  1 means it is definitely going to happen  P < 0.05 are unusual and highly unlikely to occur

III. COMPLEMENTARY EVENTS  The sum of all probabilities in a sample space is 1.  Complement of Event: the set of all outcomes not included in E  E’ = E prime  E’ = 1 – E  Page 124 Example 7

HOMEWORK Pages 125 – 128 #2 – 32 even