LESSON: Probability Simulations Part 1
| Site: | Mountain Heights Academy OER |
| Course: | Introductory Statistics Q4 |
| Book: | LESSON: Probability Simulations Part 1 |
| Printed by: | Guest user |
| Date: | Saturday, 26 April 2025, 12:41 PM |
Theoretical vs Experimental Probability
At the beginning of the quarter we learned about two different types of probability:
Experimental Probability: This type of probability relies on repeated trials of the same experiment. For example, if I want to know the experimental probability of landing on heads when I flip a coin, I would flip a coin and record the result.
Theoretical Probability: This type of probability relies on what we expect to happen. For example, If I want to know the theoretical probability of landing on heads when I flip a coin, I would recognize that with a fair coin, landing on heads has a 50% probability.
Take a look at this video that will show the difference between theoretical and experimental probability when spinning a spinner 16 times.
Long-Run vs. Short-Run Behavior
Did you notice in the last lesson video that our experimental probability did not match what we expected to happen (the theoretical probability)?
We shouldn't be surprised by that. In the short-run (16 trials) the results can be very sporadic. However, in the long-run, we would see that the experimental probability would get closer and closer to equaling the theoretical probability. Check out the next video to see what I mean.
Using Simulations to Predict Probability
Online simulation software can be very useful to us because it helps us conduct trials of an experiment many times very quickly.
We also learned from the last lesson video that if we conduct a simulation a large number of times (known as the "long-run") that the experimental probability and theoretical probability will get closer and closer to matching.
This comes in handy when we don't know the theoretical probability. If I can simulate a large number of trials of the experiment, then I can come up with an estimate the theoretical probability.
Another Example
We don't always have to flip a coin to represent boy/girl probabilities. We can adapt many different types of simulations to fit our problem. Watch the following lesson video to see an example of how to simulate boy/girl with dice.