Simulation
In short: Simulation imitates a real chance situation with a simple random tool, such as dice, coins or random digits, and repeats it many times to estimate a probability.
7th GradeProbability7.SP.C.8c
What is Simulation?
When an event is hard to test for real, a simulation stands in for it. You pick a random device whose outcomes match the real chances, run many trials, and let the results estimate the probability.
For a player who sinks 70% of her free throws, the digits 0 through 6 can stand for a made shot and 7 through 9 for a miss, since 7 of 10 digits are made shots. One trial uses as many digits as shots. The more trials you run, the closer the estimate usually gets to the true value.
How to spot it
- A real experiment would be too slow, costly or impossible, but its chances are known.
- The problem says use a coin, die, spinner or random number table to model the situation.
- You are asked about the chance of a streak or a pattern, like three misses in a row.
- A list of repeated trial results is given and you must estimate a probability from it.
The method
- Choose a random device and assign outcomes so that their chances match the real situation.
- Define one trial: how many random results make a single run of the experiment.
- Run many trials and record whether the target event happened in each.
- Divide the number of trials with the event by the total number of trials.
Simulation: solved example
Problem
A volleyball server lands 70% of her serves. To estimate the chance she lands at least 4 of her next 5, a class runs 10 simulated trials with random digits (0 to 6 = landed). The numbers landed in the ten trials are 3, 4, 5, 2, 4, 3, 5, 4, 3, 2. Estimate the probability.
Solution
Count the trials with at least 4 landed serves: the values 4, 5, 4, 5, 4 give 5 trials.
The estimate is \(\frac{5}{10} = 0.5\), so about 50%. More trials would make this estimate steadier (the exact value is near 52.8%).
Try it
Question 1
A spinner has 4 equal colors. Which digits from a random digit table could model it, and how?
Show the answer
Let 1 to 4 stand for the colors and ignore other digits; each color then has probability \(\frac{1}{4}\) per usable digit.
Question 2
In 40 simulated trials, a streak of 3 misses occurred in 6 trials. Estimate its probability.
Show the answer
\(\frac{6}{40} = 0.15\), about 15%.
Simulation vs. Experimental Probability
Experimental probability comes from recording what truly happened in the real process. A simulation instead mimics the process with a stand-in tool because the real one is out of reach, and then computes an experimental-style fraction from the model. Both rely on repeated trials, but only one touches the real thing.
Keep going
Lessons
Worksheets and quizzes
- Compound Events and Simulations – Worksheet
- Compound Events and Simulations – Quiz
- Probability and Probability Models – Worksheet
- Probability and Probability Models – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Probability