Chapter 5: Elementary Probability Theory 5.1 – What is Probability 5.2 – Some Probability Rules – Compound Events 5.3 – Trees and Counting Techniques

“How Often Do Lie Detectors Lie?” Focus Problem “How Often Do Lie Detectors Lie?” Read page 159=160 in text book

5.1 – What is Probability? Numerical measure between 0 and 1 that describes the likelihood that an event will occur. 0 ≤ P(A) ≤ 1 P(A) = Probability of “event A” If P(A) = 0, the event is certain NOT to occur If P(A) = 1, the event is certain to occur

Probability Assignments Intuition: incorporates past experience, judgment, or opinion to estimate the likelihood of an event. Relative Frequency: uses the formula, 𝑓 𝑛 where f is the frequency of the event occurrence in a sample of n observations. Equally Likely Outcomes: uses the formula, Number of outcomes favorable to an event Total number of outcomes

Guided Exercise #1 As whole group, turn to page 161-162 Look-over answers Whole group clarification

Vocabulary Law of Large Numbers: as the sample size increases and increases, the relative frequencies of the outcomes get closer and closer to the theoretical (or actual) probability value. Statistical Experiment/Obsevation: any random activity that results in a definite outcome. Event: a collection of one or more outcomes of a statistical experiment/observation. Simple Event: only one outcome Sample Space: set of all simple events of an experiment/observation. Sum of the probabilities of all simple events in a sample space must = 1

Guided Exercise #2 As whole group, turn to page 163-164 Cover answers Whole group clarification

More Vocabulary Complement of Event A (Ac): event that “A” does not occur. P(A) + P(Ac) = 1 P(Ac) = 1 – P(A)

Guided Exercise #3 As whole group, turn to page 165 Cover answers Whole group clarification

Checkpoint Assign probabilities to events Explain how the law of large numbers relates to relative frequencies Apply basic rules of probability in everyday life. Explain relationship between statistics and probability

Homework Read Pages 160-166 Do Problems Take notes on what we have not covered Do Problems Page 167-169 (1-11) odds Check odds in back of book Read and preload 5.2 information Notes/vocab