Sec. 5.3: SIMULATING EXPERIMENTS

CHAPTER 5: PRODUCING DATA

To simulate problems of chance with the help of a random number table.

To simulate problems of chance using the calculator.

OBJECTIVES

THREE METHODS OF SIMULATION TO ANSWER QUESTIONS INVOLVING CHANCE

1. Try to estimate the likelihood of a result by actually carrying out the experiment.

Slow, sometimes costly, and often impractical

2. Develop a probability model and use it to calculate a theoretical answer.

Requires knowing some rules of probability (we will do this in chapter 6)

3. Start with a model that, in some fashion, reflects the truth about the experiment, and then develop a procedure for simulating of repetitions of the experiment.

Use table B or a computer software program

SIMULATION

The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration, is called a simulation. For example, you could use a coin or a die to

represent the simulation of having a boy or a girl since the theoretical probabilities are the same.

Independent (trials) – One event has no effect or influence over the next Coin tosses, spinning a wheel, rolling a die, etc.

SIMULATION STEPS

Step 1: State the problem or describe the experiment.

Step 2: State the assumptions.

Step 3: Assign digits to represent outcomes.

Step 4: Simulate many repetitions.

Step 5: State your conclusions.

See example 5.21 on p.310-311

EXAMPLE 5.22- ASSIGNING DIGITS PART A

Choose a person at random from a group of which 70% are employed. One digit simulates one person.

For example:0, 1, 2, 3, 4, 5, 6 = employed

7, 8, 9 = not employed

Note: Other numeric assignments may be used but always try to use the most efficient set.

Choose one person at random from a group of 73% are employed. Now two digits simulate one person:

For example:00, 01, 02, . . . . , 72 = employed

73, 74, 75, . . . . , 99 = not employed

EXAMPLE 5.22- ASSIGNING DIGITS PART B

Choose one person at random to form a group of which 50% are employed, 20% are unemployed, and 30% are not in the labor force. There are now three possible outcomes, but the principle is the same. One digit simulates one person:

For example:0, 1, 2, 3, 4 = employed

5, 6 = unemployed 7, 8, 9 = not in the labor force

EXAMPLE 5.22- ASSIGNING DIGITS PART C

ASSIGNING DIGITS NOTE

You may use multiple assigning methods, but ALL digits need to be accounted for. For example:

Rock: 0, 1, 2 Paper: 3, 4, 5 Scissors: 6, 7, 8 Skip 9

See example 5.23 on p.312-313

Homework: p.313-317 #’s 59, 63, & 72 P.320-322 #’s 75, 79, 81, 83 & 85