Finite Math - Sets of Outcomes and Trees
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The document explains the concepts of random experiments, sample spaces, and tree diagrams, illustrating these ideas with examples and quizzes. It also covers the multiplication principle for calculating the number of outcomes in multi-stage experiments. Additionally, it promotes resources for further learning, including recorded lectures and practice problems.
Finite Math - Sets of Outcomes and Trees
- 1. 1.4 Sets of Outcomes and Trees
- 2. Random Experiment and 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. Tree Diagram Tree Diagrams are a useful way to visually represent a multi-stage experiment and determine the sample space.
- 4. How to make 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. Tree Diagram The branches of a tree represent outcomes of a particular stage. I personally like to line up the outcome from the same stage vertically:
- 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. 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. Quiz 1.4.1
- 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. 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. 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. 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. 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. 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. Summary Definition: Random experiment Sample space How to make a Tree Diagram determine sample space Multiplication Principle
- 16. Features 27 Recorded Lectures Over 116 practice problems with recorded solutions Discussion boards/homework help Visit finitehelp.com to find out more For special offers and additional content... Follow us on twitter @finitehelp Become a fan on Facebook