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
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, 鍖ipping 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. Lets 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, theres 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 entr辿e, 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 entr辿e, 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 De鍖nition: Random experiment Sample space How to make a Tree Diagram determine sample space Multiplication Principle