Simulation of Random Events
Simulation is a way to model random events, such that
simulated outcomes closely match real-world outcomes. By
observing simulated outcomes, researchers gain insight on
the real world.
View Video Lesson
Why use simulation?
Some situations do not lend themselves to
precise mathematical treatment. Others may be difficult,
time-consuming, or expensive to analyze. In these situations,
simulation may approximate real-world results; yet, require less
time, effort, and/or money than other approaches.
How to Conduct a Simulation
A simulation is useful only if it closely mirrors real-world
outcomes. The steps required to produce a useful simulation
are presented below.
- Analyze the simulated outcomes and report results.
Note: When it comes to choosing a source of random numbers
(Step 3 above), you have many options. Flipping a coin and
rolling dice are low-tech but effective. Tables of random numbers
(often found in the
appendices of statistics texts) are another option. And good
random number generators can be found on the internet.
Random Number Generator
When you need random numbers, coin flipping, dice rolling, and random number tables can be cumbersome, particularly
with large samples. As an alternative, use Stat Trek's Random Number
Generator. With the Random Number Generator, you can select up to 1000 random
numbers quickly and easily. The Random Number Generator is free. It can found in the Stat Trek
main menu under the Stat Tools tab. Or you can tap the button below.
Random Number Generator
Simulation Example
In this section, we work through an example to show how to
apply simulation methods to probability problems.
Problem Description
On average, suppose a baseball player hits a home run once in every 10
times at bat, and suppose he gets exactly two "at bats" in every game.
Using simulation, estimate the likelihood that the
player will hit 2 home runs in a single game.
Solution
Earlier we described seven steps required to produce a useful
simulation. Let's apply those steps to this problem.
Random Numbers |
42 99 02 65 04 14 30 09 70 88 89 85 95 40 53 67 25 50 48 79 86 92 76 24 53 39 08 73 78 17 72 81 08 01 68 94 43 43 95 12 36 90 28 88 34 69 18 69 91 79 14 82 26 94 15 26 19 41 74 02 17 20 38 84 74 30 34 96 09 46 61 41 02 93 94 90 00 71 84 98 30 82 80 11 92 97 81 29 85 44 40 05 83 22 04 86 13 33 00 99 74 75 27 43 68 22 59 20 66 00 24 01 96 84 19 14 57 26 47 58 51 73 06 08 49 52 70 15 79 35 65 28 40 77 93 73 33 24 25 22 32 03 89 03 62 13 85 16 23 28 12 61 16 75 45 37 15 54 36 18 45 64 31 31 06 80 32 75 99 27 91 25 98 05 55 32 27 16 51 45 89 31 78 90 82 05 11 39 80 83 01 20 10 67 97 33 72 09 98 78 39 56 57 54 63 35 21 35 93 18 17 48 55 60 44 92 21 07 77 42 46 86 41 49 76 96 36 62 38 11 64 07 04 58 23 56 29 37 87 37 59 47 83 77 21 63 10 95 87 10 42 71 12 88 06 52 42 99 02 65 04 14 30 09 70 88 89 85 95 40 53 67 25 50 48 79 86 92 76 24 53 39 08 73 78 17 72 81 08 01 68 94 43 43 95 12 36 90 28 88 34 69 18 69 91 79 14 82 26 94 15 26 19 41 74 02 17 20 38 84 74 30 34 96 09 46 61 41 02 93 94 90 00 71 84 98 30 82 80 11 92 97 81 29 85 44 40 05 83 22 04 86 13 33 00 99 74 75 27 43 68 22 59 20 66 00 24 01 96 84 19 14 57 26 47 58 51 73 06 08 49 52 70 15 79 35 65 28 40 77 93 73 33 24 25 22 32 03 89 03 62 13 85 16 23 28 12 61 16 75 45 37 15 54 36 18 45 64 31 31 06 80 32 75 99 27 91 25 98 05 55 32 27 16 51 45 89 31 78 90 82 05 11 39 80 83 01 20 10 67 97 33 72 09 98 78 39 56 57 54 63 35 21 35 93 18 17 48 55 60 44 92 21 07 77 42 46 86 41 49 76 96 36 62 38 11 64 07 04 58 23 56 29 37 87 37 59 47 83 77 |
The simulation predicts that this particular player will hit consecutive home
runs 6 times in 500 games. Thus, the simulation suggests that
there is a 1.2% chance that he will hit two home runs in a single game.
The actual probability, based on the
multiplication rule, states that there is a 1.0% chance that this player
will hit consecutive home runs in a game. While the simulation is not exact,
it is very close. And, if we had generated a list with more
random numbers, it likely would have been even closer.