Page 189 - Probability Demystified

178 CHAPTER 10 Simulation

Random devices are items such as dice, coins, and computers or calculators.
These devices generate what are called random numbers. For example, when a
fair die is rolled, it generates the numbers one through six randomly. This
means that the outcomes occur by chance and each outcome has the same
probability of occurring.
Computers have played an important role in simulation since they can
generate random numbers, perform experiments, and tally the results much
faster than humans can. In this chapter, the concepts of simulation will be
explained by using dice or coins.

The Monte Carlo Method

The Monte Carlo Method of simulation uses random numbers. The steps are

Step 1: List all possible outcomes of the experiment.
Step 2: Determine the probability of each outcome.
Step 3: Set up a correspondence between the outcomes of the experiment
and random numbers.
Step 4: Generate the random numbers (i.e., roll the dice, toss the coin,
etc.)
Step 5: Repeat the experiment and tally the outcomes.
Step 6: Compute any statistics and state the conclusions.
1
If an experiment involves two outcomes and each has a probability of ,
2
a coin can be tossed. A head would represent one outcome and a tail the
other outcome. If a die is rolled, an even number could represent one
outcome and an odd number could represent the other outcome. If an
1
experiment involves five outcomes, each with a probability of , a die can be
5
rolled. The numbers one through five would represent the outcomes. If a six
is rolled, it is ignored.
For experiments with more than six outcomes, other devices can be used.
For example, there are dice for games that have 5 sides, 8 sides, 10 sides,
etc. (Again, the best device to use is a random number generator such as a
computer or calculator or even a table of random numbers.)

EXAMPLE: Simulate the genders of a family with four children.

SOLUTION:

Four coins can be tossed. A head represents a male and a tail represents
a female. For example, the outcome HTHH represents 3 boys and one girl.