Sec. 5.3: SIMULATING EXPERIMENTS C HAPTER 5: P RODUCING D ATA

To simulate problems of chance with the help of a random number table. To simulate problems of chance using the calculator. O BJECTIVES

T HREE 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

S IMULATION 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.

S IMULATION S TEPS 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

E XAMPLE A SSIGNING D IGITS P ART 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 E XAMPLE A SSIGNING D IGITS P ART 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 E XAMPLE A SSIGNING D IGITS P ART C

A SSIGNING DIGITS N OTE 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

Homework: p #’s 59, 63, & 72 P #’s 75, 79, 81, 83 & 85