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Introduction and requirements
Introduction and requirements
Standard 91268 is worth 2 credits and is about ways of simulating situations involving chance.
The 2MAS students will be using simulations as part of the lead in to studying theoretical probability (the external topic for the 2MAS course).
Any errors or links that don't work please let your teacher know - or email rouwejan@ashs.school.nz or cforster@ashs.school.nz
Assessment information
Assessment information
In this standard, you will be answering a probabilistic question by planning and running an experiment.
You will do this via the following steps:
Identify the question to be answered from the situation.
Describe the tool(s) that you will use to run your experiment.
Describe how you will simulate the situation using your tool(s) and plan the full experiment.
Identify and describe assumptions you have made when planning your simulation.
Run the simulation and collect data.
Calculate and describe the experimental probability and an appropriate mean.
Answer the question, and discuss the effects your assumptions would have on your answer.
In this unit, we will learn how to find the experimental probability of an event occurring by running many simulations.
The recommended way to learn this unit is to work on a practice task as you learn the content, one section at a time.
At the bottom of the page are some additional practice tasks, but for learning the content it is recommended that you work on the Coca Cola Promotion activity. Make a copy of the activity, then get started with learning the content.
Extra Resources:
Liz Sneddon Youtube Playlist - Full video example that you can follow along with.
LESSONS
LESSONS
Problem & Plan - I can plan a trial to answer an investigative question.
Problem & Plan - I can plan a trial to answer an investigative question.
...with relational thinking - I can identify and explain assumptions I have made when designing a trial.
...with relational thinking - I can identify and explain assumptions I have made when designing a trial.
Summary of Problem and Plan
Write down a probabilistic problem about the scenario that you want to solve.
Describe your Assumptions (Merit+).
Identify your chosen tool to create your trials.
Describe your simulation. What does a single trial look like? What counts as a success? How many trials will you do?
Key words
Key words
Trial - One round of the situation. In the white car example, one trial is when 10 cars have passed.
Assumption - You are not explicitly told every detail about the situation. Describe anything you need to assume about the situation before you can start your simulation.
Data - I can run a trial using an appropriate tool.
Data - I can run a trial using an appropriate tool.
To run your simulation, you need to set up a spreadsheet as you described it in your plan.
The next job is to obtain the random numbers that simulate your situation to populate your spreadsheet. There are several methods you can choose from for this option.
Using Spreadsheets to make the numbers
Using Spreadsheets to make the numbers
The RANDBETWEEN() function creates a random number between two numbers.
Randbetween(1, 10) will create a random integer between 1 and 10.
Note: The random number will constantly change. To stop it from changing, copy all of the random numbers then special paste values only.
Shortcut for "values only" paste is:
Ctrl + Shift + V or ⌘ + Shift + V
Using dice, cards etc
Using dice, cards etc
Set up a spreadsheet to enter the data. Then start rolling the dice, drawing cards or whatever other method you decided to use to obtain your random numbers, and enter the data into the spreadsheet.
You will need to first calculate how many random numbers you need in total. (Number of trials x How many numbers per column).
Then follow the instructions on the website.
Once you have the numbers, copy/paste them into a spreadsheet.
Useful Spreadsheet Formulae (Optional, but might make your life easier)
Generate Random Number
=RANDBETWEEN(1,10)
This generates a random whole number between 1 and 10.
Sum
=SUM(A3:A10)
This will add up all the numbers between cells A3 and A10.
Count if
=COUNTIF(C2:F2, ">=3")
This will count how many numbers between the cells C2 and F2 are 3 or greater.
If statement
=IF(A3>=4, "YES", "NO")
This checks whether the cell A3 is 4 or more. If it is, the cell will write YES. If it isn't, the cell will write NO.
Analysis - I can calculate the mean of a set of numbers, and explain what it means
Analysis - I can calculate the mean of a set of numbers, and explain what it means
Apart from finding the probability, you want to calculate an average (mean).
To do this, you should count something other than the objective in each trial. Ideally, you should count something that is somewhat relevant to the main topic. Then, you calculate the mean of those counts.
In the White Car example, I counted how many cars had to go past to get four white cars. Naturally, this could only be counted in the rounds where there were four white cars. Then, I calculated the mean (by adding up all of the counts, and dividing by the number of counts, which was 9) and I got a mean of 7.2 cars.
This means that when Jimmy won, on average he would win on the 7th or 8th car.
Calculating the Mean (average)
Mean = (Sum of counts) ÷ (how many counts there are)
Conclusion - I can find the experimental probability of an event using data from a trial, and use it to answer a question
Conclusion - I can find the experimental probability of an event using data from a trial, and use it to answer a question
Finding the Experimental Probability
Once you have completed all of your trials, you need to check each one to see what the outcome was. Outcomes might be win or lose, success or fail, Yes or No etc.
Then, to find the experimental probability, count how many favourable outcomes there are and divide that by the total number of outcomes. The decimal is your experimental probability, and to turn it into a percentage you multiply it by 100.
White Car example:
Out of 50 trials, Jimmy would have won his bet 9 times. This means that the experimental probability of Jimmy winning the bet is 9 out of 50, or 9/50.
9 ÷ 50 = 0.18
0.18 x 100 = 18%
The probability of Jimmy winning the bet is 0.18, or 18%.
---------------------------CHECKPOINT--------------------------
---------------------------CHECKPOINT--------------------------
The rest of the website has relational and extended abstract question. It makes little sense to work on those if you are still struggling with the skills above.
Self-evaluation: If you are confident with the following, then you can continue:
You can plan a trial to answer a question.
You can use a valid method to run and record your simulation (valid methods is your choice of dice, cards, spreadsheet or Random.org)
You can calculate the mean and experimental probability from collected data.
You can use the experimental probability answer the question.
Extended Abstract - I can run a full simulation to answer a probabilistic question, justifying the assumptions made along the way and discussing the impact they would have on the experimental probability.
Extended Abstract - I can run a full simulation to answer a probabilistic question, justifying the assumptions made along the way and discussing the impact they would have on the experimental probability.
Assumptions and Independent Probability slides
Tools
Tools
RESOURCES - use the links below to find resources that will help you practice the skills you need to learn
RESOURCES - use the links below to find resources that will help you practice the skills you need to learn
Practice Investigations & Activities
Practice Investigations & Activities
1) Oil wells & 2) Cereal Temptations
1) Oil wells & 2) Cereal Temptations
Oil Wells practice assessment
Cereal Temptations practice task
3) Beetle game
3) Beetle game
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