SimulationsSection 5.1 in your book…

Simulation:◦ A simulation is an imitation of chance behavior,

most often carried out with random numbers.

Random:◦ When we are given a number of previous

outcomes we cannot predict the next outcome.

Definition

Rolling a Die Flipping a Coin Random Number

Table (refer to as Table D)

RandInt (on the calculator) The command is

RandInt(first,last,times) Pulling a card (or

cards) from a deck of cards

Common Methods for simulation:

A couple wants to have a boy to carry on the family name. If they keep having children until they get a boy what is the probability that they will have boy before they have five children?

Assign H – boy and T – girl Flip a coin 5 times and record your results Do this experiment 20 times and record

Got Pennies?

On average, how many children did the couple have before they had a boy? ◦ If your result was GGBGB you would label that

result line as 3 because the third child was a boy.◦ Average your 20 lines.

◦ Come and list your averages:

◦ Class average:

Results?

Go to page 290 and read the green box with “Golden Ticket Parking Lottery”

What is the probability that a fair lottery would result in 2 winners from the same class?

Use Table D◦ Label AP students O1-28◦ Label all other students 29-95

Table D Example

How do I use this table?

Each box of cereal contains 1 collectible card. There are 5 different collectible cards available, each with a different driver.

Each of the 5 cards are equally likely to be in your cereal box.

What is the probability that it will take 23 or more boxes to get a full set of 5 NASCAR collectible cards?

RandInt

Label 1 – Jeff Gordon Label 2 – Dale Earnhardt, Jr Label 3 – Tony Stewart Label 4 – Danica Patrick Label 5 – Jimmie Johnson

RandInt(1,5) simulates buying one box of cereal and looking at the card.

Since we want a full set of cards, we will keep pressing enter until we get all five labels from 1-5 and record how many times it took*

How do I use my calculator?

Do this 10 times and record how many boxes it took you each time.

Did anyone have to buy more than 22 boxes before you got all 5 cards?

The probability that it will take 23 boxes of cereal before collecting all 5 cards is roughly 0.

Results

State: What is the question of interest about some chance process?

Plan: Describe how to use a chance device to imitate one repetition of the process. Explain clearly how to identify the outcomes of the chance process and what variable to measure.

Do: Perform many repetitions of the simulation.

Conclude: Use the result of our simulation to answer the question of interest.

4 Step Process (in case you see a little staircase in the book and wonder what they are wanting you to do!)

This is the bookwork for the chapter…we will go over the stuff from 5.1 tomorrow, so keep up! Page 293 (1-4, 7-12, 14-20, 23-27) Page 309 (39-46, 49-56) Page 329 (63, 65, 67-78, 81, 83-88,

94-96, 99-103)

Homework

There are 4 marbles in a bag (blue, red, green, yellow). What is the probability that you choose a yellow marble?

If you are assigning students to 6 groups in a class, what is the probability that a group ends up with all members being girls?

You have a choice of 3 colleges to attend. If you wanted to randomly choose, what is the probability that you chose the one that was in state?

Given this situation, what simulation would you choose and why?