probability: making choices

Making Choices Using Organized Lists, Tree Diagram, and the Counting Principle : 

Making Choices Using Organized Lists, Tree Diagram, and the Counting Principle

Organized Lists : 

Organized Lists When making choices, sometimes it is best to make an organized list. To make a list, you first write down all of the offered choices. For example if you had a pair of jeans, a pair of shorts and 3 shirts: red, blue, and white how many different outfits could you make with these different choices of clothing? You could start by writing down on a “T” chart the bottoms that you have. Your “T” chart would show jeans on the right and shorts on the left. Under each of these 2 categories on the chart you would write: red, blue and white. This shows that for both jeans and shorts, you could wear each of the shirts: red, blue, and white.

Slide 3: 

Organized list example w/ T chart: Organized list example w/out a chart: This shows that for both jeans and shorts, you could wear each of the shirts: red, blue, and white. This is one way to make a simple organized list. Also know that using the “T” chart is not always necessary especially when you have more than 2 category choices. Once you get great at it, you can skip using it and just write the outcomes in a list. Jeans Shorts Red Blue White Red Blue White Here is a video example of making an organized list that does not use a “T” chart. 1. Shorts, red top 4. Jeans, red top 2. Shorts, blue top 5. Jeans, blue top 3. Shorts, white top 6. Jeans, white top

Tree Diagram : 

Tree Diagram Another way to use math to make choices is through using a tree diagram. A tree diagram is similar to an organized list except instead of writing your choices on a chart or as a list, you branch it out similar to a story web. Using the same situation as in the first method of figuring out how many different outfits you may have with all of the possible choices you would write down the category with the least amount of choices. We have already identified that category as “bottoms”, so your jeans and shorts. After you write down the first bottom of jeans, you then draw out from the word jeans three tree branches. Attached to each branch are the words red, blue, and white to represent the possible shirts you may wear with your jeans. Next, follow the same procedures with your shorts category.

Slide 5: 

Tree Diagram example: Jeans Blue White Red Shorts Red Blue White Here is video example of how to find all possible outcomes using the tree diagram method.

Counting Principle : 

Counting Principle The last way to use math in making choices is called “The Counting Principle”. The counting principle is the easiest way to find the amount of choices possible but it does not show you the specific possibilities just as the other 2 methods do. This method can only be used if you want to find out how many choices there were total. If you wanted to find out the exact choices, you would have to make an organized list or use the tree diagram. To use the counting method, count up how many choices that are in each category. Then multiply the amount in each category to get the total amount of choices possible.

Counting Principle example: : 

Counting Principle example: Since there are 2 choices for bottoms one being jeans and the other being shorts you multiply 2 by the 3 types of tops; red, blue and white. The product 6 is the total amount of choices possible. 2 x 3 = 6 possible outfits bottoms tops Here is a video example of the counting principle.

Think you got it yet? : 

Think you got it yet? Before we move on, here is a another video example of all 3 methods together. See if you can follow along.

Let’s Practice! : 

Let’s Practice!

Problem #1 : 

Problem #1 You are at a carnival where you can create a candied apple of your choice. You can choose one from each of the following 2 categories: sauces, and toppings. For sauces, you also have 2 choices, caramel or red candy. Next, for toppings you have the choice of peanuts, walnuts, or chocolate sprinkles. Using each of the methods , find all of the possible candy apple variations you could choose to make. When you have found answers for each method, click to the next slide to see if you were right. Take your time and double check your work. Go back to the examples if you have to. Good luck!

Answers to Problem #1 : 

Answers to Problem #1 List: Tree: Counting: 2 x 3 = 6 sauces toppings outcomes Caramel Red Candy peanuts walnuts sprinkles peanuts walnuts sprinkles Caramel Red Candy peanuts walnuts sprinkles peanuts walnuts sprinkles How did you do? Try another one!

Problem #2 : 

Problem #2 You are at your local deli sandwich store. You want to make a sandwich. You have to choose from various types of bread, cheeses, and meats. Vegetables and spreads are unlimited. For bread, you may choose from wheat or white. For cheeses, you can choose from American, Swiss or Pepperjack. Finally meats you may choose from ham, turkey, or tuna. How many different sandwich variations could you make? Go back and review all the methods if you forgot. Double check your work and try your best!

Answers to Problem #2 : 

Answers to Problem #2 List: 1. Wheat bread, American Cheese, Ham 2. Wheat bread, Swiss Cheese, Ham 3. Wheat Bread, Pepperjack, Ham 4. Wheat bread, American Cheese, Turkey 5. Wheat bread, Swiss Cheese, Turkey 6. Wheat Bread, Pepperjack, Turkey 7. Wheat bread, American Cheese, Tuna 8. Wheat bread, Swiss Cheese, Tuna 9. Wheat Bread, Pepperjack, Tuna 10. White bread, American Cheese, Ham 11. White bread, Swiss Cheese, Ham 12. White Bread, Pepperjack, Ham 13. White bread, American Cheese, Turkey 14. White bread, Swiss Cheese, Turkey 15. White Bread, Pepperjack, Turkey 16. White bread, American Cheese, Tuna 17. White bread, Swiss Cheese, Tuna 18. White Bread, Pepperjack, Tuna

Tree Diagram: : 

Tree Diagram: Ham American Turkey Tuna Ham Wheat Swiss Turkey Tuna Ham Pepperjack Turkey Tuna Ham American Turkey Tuna Ham White Swiss Turkey Tuna Ham Pepperjack Turkey Tuna

Counting Principle: : 

Counting Principle: 2 x 3 x 3 = 18 bread cheeses meats possible choices sandwich outcomes

References : 

References Teachertubemath. (2009, August 25). Counting Principle [Video file]. Retrieved from http://www.youtube.com/watch?v=oqjBE-eEgGA&feature=player_embedded. TenMarks Instructor. (2010, March 18). Make an Organized List for Probability, [Video file]. Retrieved from http://www.youtube.com/watch?v=tc6F54fbLRU. JAMSRoom25. (2008, April 29). Making Tree Diagrams for Possible Outcomes Part 2 [Video file]. Retrieved from http://www.youtube.com/watch?v=qEktCLb0m_A&feature=player_embedded. Mindbitesdotcom. (2009, December 03). Perms & Combs: Fundamental Counting Principle [Video file]. Retrieved from http://www.youtube.com/watch?v=md1Ct7yInuQ&feature=player_embedded.