Project Title

What are the Chances of That?

 

Introduction

Probability is the unseen factor behind the hundreds of decisions you make every day.  In daily decision-making you use experimental probability without even realizing it. Based on your past experiences, you calculate whether taking a certain action is worth the risk, or in algebraic terms, what the chance is of having a favorable outcome. You use theoretical probability when you either haven’t experienced a certain situation before or you are looking for the likelihood of something occurring in a perfect world.

 

When calculating probability in your mind, most times you don’t even think of it as math; still, it’s there just the same. Probability asks you, “What are the chances of that?”

 

Task

Working together with your group, you will first design a probability experiment.  You will want to design something that will be fun to test and interesting to watch on video.  Your end product will be a video made on either Microsoft Movie Maker or iMovie.  Experiments that require some degree of silliness can be fun to perform and to watch.  Consider experimenting both on your classmates and your teachers.  Be sure to also consider the mathematics behind your experiment, as you will be required to calculate the theoretical probability. 

 

Instructions

Complete each problem in order, keeping detailed notes along the way.  Don’t forget to capture video of the action.

 

1                     First problem:  Design Experiment 

 

·                     You have encountered probability questions about pulling marbles from a bag, selecting cards (with and without replacement), and rolling die.  These are all situations that you may want to include in your experiment, but they are certainly not the only materials that can be used.  Think creatively!  What fun materials could you use to perform a probability experiment?  Make a list and discuss the materials with your group.

 

·                     Choose one or two materials from the list and begin discussing the sample spaces that would occur with the given materials.  For instance, if I had a red, blue and green tile in a bag, and I wanted to select two tiles, then the sample space would be:   

 

RG       RB        GR       GB       BR        BG

 

·                     Once you have defined your sample space, discuss what outcome you would like to choose as your desired outcome for the experiment.  If my desired outcome is choosing a red tile and then a green tile, the theoretical probability would be .  The probability would be written P (red, then green). 

 

Hint:  If you choose two materials to work with, you will also need to calculate the probability of the second event.

 

·                     Write down a list of necessary materials, the sample space, and your desired outcome for the experiment.  Make sure to get approval from your teacher before moving on to the next step.

 

2                     Second problem:  Calculate Theoretical Probability

 

·                     Now calculate the theoretical probability of the desired outcome of your experiment.  Remember to account for replacement and non-replacement and multiply the probabilities of compound events.  Show your work carefully as you will display the theoretical probability in your finished movie.

 

Hint:  If I wanted to add flipping a coin to my experiment with the colored tiles in the bag, I would need to determine if I was looking for a heads or a tails.  Let’s say I wanted heads.  The probability would then be written as follows:

P (red, then green, heads) =

 

 

3                     Third problem:  Gather Experimental Data

 

·                     Now that your theoretical probability has been calculated, you should know how many times your experiment would need to be performed in order to achieve your desired outcome.  In the case of the tiles and the coin, if everything works perfectly, I should get the outcome once every twelve times.  Knowing that not everything is perfect, it will be important to perform the experiment more than twelve times.  In fact, you will want to perform your experiment 50 times.  Fifty will allow you to collect a substantial amount of data and it is an easy number to work with when tabulating your data.

 

·                     Create a data table to record the outcome of each of your 50 experiments.  Once your table is completed, begin experimenting.  Don’t forget to capture video clips of each of your subjects performing the experiment. 

 

4                     Fourth problem:  Compare

 

·                     Sort your data and compare each experimental outcome to the theoretical outcome.  You will need to create a data table to compare the probabilities.  A sample data table follows: 

 

 

·                     According to the table above, my desired outcome of drawing a red marble, followed by a green marble, and then getting a heads on the coin flip, was achieved 4 out of 50 times.  This gave a percentage of 8%.  The theoretical probability for that outcome is 1 out of 12 or approximately 8.3%.  In this case, the experimental probability and theoretical probability were very close.  This is not always the case.    

 

·                     Compare your experimental probability to the theoretical probability.  Were some of the other outcomes substantially lower or higher than you expected? 

 

·                     If you were to perform the experiment over again, what changes might you make to have your experimental data more closely mirror the theoretical probability? 

 

Conclusion 

For the conclusion of the project, you will make a video on Movie Maker or iMovie.  Use the rubric as a guide to what should be included in your video.  A successful project will mix the mathematics with video clips of students and teachers performing the experiment.  Don’t forget to clearly define what you are studying at the beginning of the video and wrap up the video with a data table and discussion of your results. 

 

The following are basic directions for Movie Maker:

 

Capturing Video from Digital Video Camera

1. Open Windows Movie Maker

2. Attach the camera to the computer using a firewire or USB cable

3. Choose “capture from video device”

 

Making a Movie with Movie Maker

On the bottom you can view your work as a “storyboard” or as a “timeline”. The

“storyboard” view is easy to use for adding the titles, pictures, videos and transitions.  When you want to add audio, music or narration, you must be in “timeline” view.

 

Playing the video clips

1. Notice the “split” button on the right. You can split

video clips to take off unnecessary sections of your video.

2. Once you have the video clips the way you want them, you can drag them down onto the timeline or storyboard view.

 

Adding a Title

1. Under Tools, Titles and Credits, choose “title at the beginning”

2. Enter the text of the title

3. Now, on the same page where you entered the text for the title, click the link “Change title animation”

4. Click “Change the text, font and color” link

5. Finally choose “Done, add title to movie”

 

Adding music to your video

1. Now in Movie Maker – choose “Import audio or music” (on the left task bar)

2. Go to the “my music” folder and choose the music you want

3. Now you can drag your music to the correct place on the timeline (again you can shorten the music – by resizing it from the right end – if the song is too long)

 

Now you are ready to make the movie

1. Get everything just how you want it in Movie Maker

2. Choose File “Save Movie File”

 

Additional help on Movie Maker can be found at:

http://www.microsoft.com/windowsxp/using/moviemaker/default.mspx

http://www.saskschools.ca/resources/techref/moviemaker/movie.html

 

Help for iMovie can be found at:

http://www.bgsu.edu/downloads/cio/file17748.pdf

http://www.apple.com/ilife/tutorials/ - imovie

 

Hint:  One of the best ways to learn the programs is to play around with the features.  Work together and help each other out.  If you know how to do transitions, help a neighboring group.  If they know how to import music, they can then help you.

 

 

Collaboration

Show your project-in-the-making to a neighboring group.  Allow the neighboring group to give constructive feedback about changes that could be made before finalizing the product.  Then watch the other group’s project and give feedback.  The goal is to help enhance the other group’s project before it is time to turn it in.  Sometimes just seeing another group’s product can give you ideas to enhance your own project.    

 

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

Score	Content	Presentation
4	The desired outcome to be studied during the project is clearly identified and stated.  Professional looking and accurate representation of the data in tables, including labels and titles is present.   The theoretical probability of the desired outcome is correctly figured with all math work shown. Conclusion includes discussion of the comparison between experimental and theoretical probabilities.	Your project contains information presented in a logical and interesting sequence that is easy to follow.   Makes excellent use of font, color, graphics, effects, etc. to enhance the presentation.   Many different "takes", camera angles, sound effects, and/or careful of use of zoom provides variety in the video. Product shows a large amount of original thought. Ideas are creative and inventive.
3	The desired outcome to be studied during the project is identified, but is stated in an unclear manner. Accurate representation of the data in tables, including labels and titles is present.   The theoretical probability of the desired outcome is figured with all math work shown.  Minor errors may be noted.  Conclusion compares experimental and theoretical probabilities.	Your project contains information presented in a logical sequence that is easy to follow.   Makes good use of font, color, graphics, effects, etc. to enhance the presentation.   Several (3-4) different "takes", camera angles, sound effects, and/or careful of use of zoom provides variety in the video. Product shows some original thought. Work shows new ideas and insights.
2	The desired outcome to be studied during the project is partially identified, and/or is stated in an unclear manner.   Accurate representation of the data is in written form, but no tables are presented.   The theoretical probability of the desired outcome is given, but no work is shown.  Major errors may also be noted.  Conclusion compares experimental and theoretical probabilities.	Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.   Makes use of font, color, graphics, effects, etc. but occasionally these detract from the presentation content.   One or two different "takes", camera angles, sound effects, and/or careful of use of zoom provides variety in the video.  It uses other people's ideas (giving them credit), but there is little evidence of original thinking.
1	The desired outcome to be studied during the project is erroneous or irrelevant.  Data tables are not shown or are inaccurate.   The theoretical probability is missing or major errors are noted. Does not compare experimental and theoretical probabilities.	Your project is difficult to understand because there is no sequence of information.   Use of font, color, graphics, effects etc. is evident but these often distract from the presentation content.   Little attempt was made to provide variety in the video.  Uses other people's ideas, but does not give them credit.

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The NROC Project 2019