Chapter 5: Elementary Probability Theory

5.1 – What is Probability5.2 – Some Probability Rules – Compound

Events5.3 – Trees and Counting Techniques

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,

– where f is the frequency of the event occurrence in a sample of n observations.

• Equally Likely Outcomes: uses the formula,

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.1. P(A) + P(Ac) = 12. 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– 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