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# Finite Math - Sets of Outcomes and Trees

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Definition:
Random experiment
Sample space

How to make a Tree Diagram
determine sample space

Multiplication Principle

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• ### Finite Math - Sets of Outcomes and Trees

1. 1. 1.4Sets of Outcomes and Trees
2. 2. Random Experimentand Sample Space A random experiment is an experiment with multiple possible outcomes. Ex: Rolling a die, ﬂipping a coin A “sample space” is the set of collection of all those outcomes. Ex: For experiment of “rolling a dice”, SS = {1, 2, 3, 4, 5, 6}
3. 3. Tree Diagram Tree Diagrams are a useful way to visually represent a multi-stage experiment and determine the sample space.
4. 4. How tomake a Tree Diagram Let use this following experiment as the example for our tree: “There is Urn A and Urn B. Urn A has balls numbered 1, 2, 3. Urn B has balls colored green and red. You choose an urn and draw a ball from it.” A B
5. 5. Tree DiagramThe branches of a tree represent outcomes of a particular stage.I personally like to line up the outcome from the same stagevertically:
6. 6.  Stage 1: Select the Urn Stage 2: Pick the Ball The resulting Sample Space is {Bg, Br, A1, A2, A3}, a total of 5 elements.
7. 7. Representing an outcome twice A common mistake many students make is to put down a repeated outcome multiple times. Let’s say there are 2 green balls in urn B. You would still only have one branch representing both green balls. Making two separate branches for one outcome is incorrect:B
8. 8. Quiz 1.4.1
9. 9. Quiz 1.4.1 Consider the following experiment: Fred goes to dinner and have to pay the bill, which comes to \$7. He has one \$10, one \$5, and three \$1. He pull random bills out of the pocket until he has enough to pay. How many elements are in the sample space? A. 9 B. 10 C. 11
10. 10. Quiz 1.4.1 Consider the following experiment: Fred goes to dinner and have to pay the bill, which comes to \$7. He has one \$10, one \$5, and three \$1. He pull random bills out of the pocket until he has enough to pay. How many elements are in the sample space? A. 9 B. 10 C. 11
11. 11. Quiz 1.4.1 Consider the following experiment: Fred goes to dinner and have to pay the bill, which comes to \$7. He has one \$10, one \$5, and three \$1. He pull random bills out of the pocket until he has enough to pay. How many elements are in the sample space? A. 9 B. 10 C. 11 Answer: C
12. 12. Multiplication principle If you have a multi-stage experiment, with equal number of possibilities in each stage regardless of the previous stage, there’s a simple way to calculate the number of element in sample space. For example, Bob goes to McDonald to get a Happy meal. He can choose cheeseburger, nuggets, or chicken sandwich for entrée, soft drink, juice or milk for the drink, and 4 different toys. The number of combinations he could get is 3 x 3 x 4 = 36. (3 entrée, 3 drinks, 4 toys)
13. 13. Quiz 1.4.2 Mike goes to subway and gets a sandwich. He can choose between 5 kinds of bread, 4 kinds of cheese, and 3 kinds of meat. How many different sandwiches does he have to choose from? A. 20 B. 60 C. 120
14. 14. Quiz 1.4.2 Mike goes to subway and gets a sandwich. He can choose between 5 kinds of bread, 4 kinds of cheese, and 3 kinds of meat. How many different sandwiches does he have to choose from? A. 20 B. 60 C. 120 Answer: B
15. 15. Summary Deﬁnition:  Random experiment  Sample space How to make a Tree Diagram  determine sample space Multiplication Principle
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