Warm-up5.1 Introduction to Probability

1) 2)3)4)5)6)7)

Student of the day!Block 1

Student of the day!Block 2

Ch. 5 Vocabulary

1) event2) complement3) probability distribution4) sample spaces5) disjoint6) mutually exclusive7) Law of Large Numbers8) Fundamental Principle of

Counting9) probability model10) Property of Disjoint

Events

11) Addition Rule of Disjoint Events

12) Addition Rule13) Conditional Probability14) Multiplication Rule15) dependent events16) independent events17) Multiplication Rule forindependent events

Important Dates on Sharepoint

Monday 12/3 5.1 to 5.3 QuizFriday 12/7 and Tuesday 12/11 Ch. 5 Notebook CheckThursday 12/13 Ch. 5 Test (2 days before Winter Break)

-----++++---- Winter Break -----+++++----After winter break:Probability ActivityMultiple Choice Practice with Ch. 5 ProbabilitySpend at least 3 days reviewing for the midterm

5.1 Introduction to Probability

Probability Distribution

Suppose we want to list the sample space of the result of flipping two coins.

If we include the probabilities it is considered a probability distribution.

The complement of any event is 1 – P(event).

What is the probability of not getting TT or what P( TTc )?

Multiplication Counting Principle

The two spinners are mutually exclusive (independent events).

Multiplication (Counting) Principle states that by multiplying thepossible outcomes in each category, we can find the total number ofpossible arrangements.

Law of Large Numbers

Let’s say you suspect your friend has unfair die. How would youactually find out if the die is weighted unequally?

Conducting a Probability SimulationThe Steps in a Simulation That Uses Random Digits 1. Assumptions. State the assumptions you are making about

how the real-life situation works. Include any doubts you might have about the validity of your assumptions.

2. Model. Describe how you will use random digits to conduct one run of a simulation of the situation. Make a table that shows how you will assign a digit (or a group of digits) to represent each possible outcome. (You can disregard some digits.) Explain how you will use the digits to model the real-life situation. Tell what constitutes a single run and what summary statistic you will record.

3. Repetition. Run the simulation a large number of times, recording the results in a frequency table. You can stop when the distribution doesn’t change to any significant degree when new results are included.

4. Conclusion. Write a conclusion in the context of the situation. Be sure to say that you have an estimated probability

Westvaco Example pg 302The ages of the ten hourly workers involved inRound 2 of the layoffs were 25, 33, 35, 38, 48, 55,55, 55, 56, and 64. The ages of the three workerswho were laid off were 55, 55, and 64, with averageage 58. Use simulation with random digits to estimatethe probability that three workers selected at randomfor layoff would have an average age of 58 or more.Assumptions

Westvaco Simulation Continued…

Model:

Repetition with Random Number Generator

• Work with a partner.• Use the random number generator to select 3

workers, find their average age write it down.• Complete this simulation 5 times.• Record your results on the classroom dotplot.

Using a Random # Table

Homework

• 5.1 P#8, 9, E#4, 8 and 9 • Read 5.2 and 5.3