~ 8.6 ~
Estimating Probabilities Using Simulation
Learning Targets
I can simulate a real-world situation using a simple experiment that reflects the probability of the actual event.
Notes
Sometimes it is easier to estimate a probability by doing a simulation. A simulation is an experiment that approximates a situation in the real world. Simulations are useful when it is hard or time-consuming to gather enough information to estimate the probability of some event.
For example, imagine Andre has to transfer from one bus to another on the way to his music lesson. Most of the time he makes the transfer just fine, but sometimes the first bus is late and he misses the second bus. We could set up a simulation with slips of paper in a bag. Each paper is marked with a time when the first bus arrives at the transfer point. We select slips at random from the bag. After many trials, we calculate the fraction of the times that he missed the bus to estimate the probability that he will miss the bus on a given day.
Activities
6.1 Which One Doesn’t Belong: Spinners
Which spinner doesn't belong?
6.3 Designing Experiments
For each situation, describe a chance experiment that would fairly represent it.
Six people are going out to lunch together. One of them will be selected at random to choose which restaurant to go to. Who gets to choose?
After a robot stands up, it is equally likely to step forward with its left foot or its right foot. Which foot will it use for its first step?
In a computer game, there are three tunnels. Each time the level loads, the computer randomly selects one of the tunnels to lead to the castle. Which tunnel is it?
Your school is taking 4 buses of students on a field trip. Will you be assigned to the same bus that your math teacher is riding on?
Add to Your Notes
Why might you want to run a simulation rather than the actual event?
Simulations are easier and usually faster to do multiple times.
If you conduct a few trial simulations of a situation and record the fraction of outcomes for which a particular event occurs, how might you know that you have done enough simulations to have a good estimate of the probability of that event happening?
When the fractions seem to not be changing very much!
Assignment
Check Google Classroom!