Part III: Gathering Data

Chapter 10: Understanding Randomness

I. Opener: Read page 267, then

A. Turn the page and pick a number at random. Write it down: ______

B. Let’s make a probability table to display all outcomes:

x / 1 / 2 / 3 / 4
P(x)

C. Were your picks really random?

D. What are the theoretical probabilities?

x / 1 / 2 / 3 / 4
P(x)

E. What are the actual probabilities in the population of all people’s picks? (See 1st paragraph on page 268)

x / 1 / 2 / 3 / 4
P(x)

II. Simulation: Definitions and Procedures

A. Simulation mimics reality by using random numbers or observable outcomes to represent real outcomes for

events or random phenomena.

B. Steps to carrying out simulation (“Ginnism”- label, table, stop, and identify)

First, Establish Correspondence (Assign something to every possible outcome.)

Next, Explain andPerformMany Repetitions in the Simulation (Tell how you will carry out each trial and show the outcomes of many trials in a clear way so someone can clearly understand your results.)

State your Stopping Rule (How many trials do you plan to carry out?)

Finally, Estimate the Probability and put it in context

III. Examples

A. “Let’s Simulate” pages 269 – 271: Suppose a cereal manufacturer puts pictures of famous athletes on cereal boxes to boost sales. 20% of the boxes will have a picture of LeBron James, 30% will have a picture of Danica Patrick, and the rest will have a picture of Serena Williams. You want all three pictures. How many boxes of cereal do you expect to have to buy in order to get a complete set?

First, Establish Correspondence: I’ll assign one-digit numbers to every possible outcome.

Next, Explain and Perform Many Repetitionsin the Simulation: I will view one digit numbers using Table B, the Random Digits Table, until I get all three athletes in a trial. I will record the # of boxes it takes to get a complete collection of athletesfor each trial.

State your Stopping Rule: I will perform ten trials in all and compile my results in the table below:

Trial Number / Outcomes / # of Boxes it took to get all three athletes
1
2
3
4
5
6
7
8
9
10

Finally, Estimate the Probability and put in context: Finally, I will collect and summarize the results of all my trials to determine the number of boxes it takes to get all three athletes in a collection of cereal boxes. We’ll make a boxplot and find some summary statistics now.

B. “For Example” page 271: The game of 21 can be played with an ordinary six-sided die. Competitors each roll the die repeatedly, trying to get the highest total less than or equal to 21. Suppose your opponent has rolles an 18. You want to beat him by getting more than 18 points without going over 21. How many rolls do you expect to make and what is your chance of winning?

First, Establish Correspondence:

Next,Explain and Perform Many Repetitions in the Simulation:

State your Stopping Rule:

Trial Number / Outcomes / Number of Rolls / Result
(Won or Lost
1
2

Finally, Estimate the Probability and put it in context:

IV. Homework: #’s 1 – 10all pages 276 – 277