Introduction
There are two types of probability: theoretical probability and experimental probability. With this investigation, you will be comparing how the two compare with one another!
Task
You will be creating two survey questions. These questions will be given to all of your classmates so that you have a set of results for both questions. You will then make probability predictions based on the data you have collected, and then run a simulation to see how accurate your predictions are.
Process
PHASE ONE
1) You need to create two survey questions:
- Each question needs to have 2 to 5 possible choices: (i.e. Do you prefer dogs or cats? What season were you born in? Do you like hockey?)
- Your questions must be fair. Everybody in the class has to be able to answer it (i.e. Avoid questions like "Who's your favourite Harry Potter character?" or "What's your favourite type of makeup?" or "Who's your favourite character in the indie game Don't Starve Together?")
- Your questions should not have an "other" option. This means everybody in the class has to choose from one of your possible outcomes
- Your two questions should be chosen to compare two things. For example, by asking "What season were you born in?" and "Do you like hockey?" I can compare to see if there's any relation between people being born in winter and people who like hockey.
Please write your questions in your math notebook, then show them to Mr. Huang to have them initialled.
2) After I have checked it, create a Google Form with both your questions.
- Make sure all of your questions are "Required"
- Make sure that your survey collects e-mail responses so that you know who filled out your survey
- Make sure you limit your survey so EACH PERSON CAN ONLY COMPLETE IT ONCE
- Just to make life easier, make sure people can't go back and edit their responses
After creating your Google Form, paste your link to your Google Form in the attached Google Sheets NEXT to your name.
3) As the Google Sheets gets populated with peoples' surveys, start completing your classmates' surveys. Yes, you should also complete your own. After completing their survey, put a "X" UNDER YOUR NAME and NEXT TO YOURS.
PHASE TWO
At this point, everybody should have completed your survey, and you've completed everybody else's survey. Complete the following NEATLY on graph paper.
1) Create a frequency table for the responses to both of your questions. Your frequency table should show me your choices and how many people chose each choice. Make sure each frequency table has a title.
2) Using your frequency tables, graph the responses for both of your questions. Each question should get its own graph. Don't forget to label your graph properly with titles, labels axes, a proper scale and using a RULER (colours would be a huge plus too!)
3) Create a tree diagram showing all of the possibilities that someone could get by answering your two questions.
4) Choose two non-mutually exclusive events from your survey and fill out the Venn Diagram template. Label the two events and give the Venn Diagram a title. Place every person in our class in your Venn Diagram. After completing this, come up with three specific observations that you noticed after comparing your two events.
PHASE THREE
Now it's testing time. Read the instructions on the attached Google Doc. Use the wheel provided to help.
After this we're done! Collect your PHASE ONE, PHASE TWO and PHASE THREE, double check your work, staple everything together and turn it in.
Evaluation
| Level 4 | Level 3 | Level 2 | Level 1 | |
| Survey Question Choice | Student creates two interesting multiple choice questions that effectively compares two variables | Student creates two multiple choice questions that somewhat compare two variables | Student creates two survey questions. The connection between both questions makes some sense. | Student creates two survey questions. The connection between both questions is weak. |
| Google Form Creation and Data Collection Process | Student follows instructions properly with the creation of their Google Form and promptly and properly logs their completion of their fellow students' surveys. Data collection with experimental data is completed properly and efficiently. | Student follows instructions with the creation of their Google Form and logs their completion of their fellow students' surveys. Data collection with experimental data is completed with some efficiency. | Student creates their Google Form and logs their completion of their fellow students' surveys with some difficulty. Data collection with experimental data is completed but lacks efficiency. | Student struggles with the creation of their Google Form and with completing their fellow students' surveys. Data collection with experimental data is completed with great difficulty. |
| Diagram and Graph Creation | Frequency Tables, Graphs and Diagrams are created with proper labels and are presented neatly and aesthetically | Frequency Tables, Graphs and Diagrams are created with proper labels. | Frequency Tables, Graphs and Diagrams are created but are missing some labels and lack neatness | Frequency Tables, Graphs and Diagrams are created but are missing several components and lack neatness |
| Data Analysis | Observational data facts are significant and correspond to the data represented in the graphs. Student makes strong connections between collected theoretical data and tested exprimental data. | Observational data facts are recorded and correspond to the data represented in the graphs. Student makes truthful connections between collected theoretical data and tested experimental data. | Observational data facts are recorded and mostly correspond to the data represented in the graphs. Student states facts about the data that demonstrates some understanding of the relationship between collected theoretical data and tested experimental data. | Observational data facts are recorded and somewhat correspond to the data represented in the graphs. Student states some facts about the data that demonstrates limited understanding of the relationship between collected theoretical data and tested exprimental data. |
| Knowledge and Understanding | Data is represted properly during graph, table and diagram creation. Probability facts are presented in the proper format, student demonstrates a thorough understanding of theoretical and experimental probability | Data is represented with few mistakes during graph, table and diagram creation. Probability facts are presented in the proper format, student demonstrates understanding of theoretical and experimental probability | Data is represented with some mistakes during graph, table and diagram creation. Probability facts are presented truthfully but not always in the proper format, student demonstrates some understanding of theoretical and experimental probability | Data is represented with mistakes during graph, table and diagram creation. Probability facts are mostly presented truthfully but often not in the proper format, student demonstrates limited understanding of theoretical and experimental probability |
Conclusion
What do you notice about the connection between theoretical data and experimental probability? Why is theoretical probability important? What are some things to consider before relying on theoretical probability?