1. UNIT 8: PROBABILITY Final Exam Review

2. TOPICS TO INCLUDE  Sample Space  Basic Probability  Venn Diagrams  Tree Diagrams  Fundamental Counting Principle  Permutations  Combinations

3. SAMPLE SPACE  Sample Space is a LIST of all of the possible OUTCOMES in a scenario  Example: Write the sample space for the types of cards that can be selected in a deck of cards  A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K  Example: List the sample space for rolling a dice  1, 2, 3, 4, 5, 6

4. SAMPLE SPACE  Now you try: List out the sample space: List the sample space for the colors in a bag of regular M&Ms

5. BASIC PROBABILITY  Probability is used a lot in a DECK OF CARDS  The DENOMINATOR should always be 52  Always REDUCE!  Example  P(black card)  P(card <4)  Answer: 26/52 or ½  Answer: 12/52 or 3/13

6. BASIC PROBABILITY  You Try: 1.P(Face Card that is not a King) 2.P(5 or a 9) 3.P(Red card or an 8)

7. VENN DIAGRAMS  Venn Diagrams are a VISUAL representation used to COMPARE data  When filling out a Venn Diagram, always START in the MIDDLE  Always check to make sure that ALL data has been used. If not, complete the diagram with a number OUTSIDE of the circles.

8. VENN DIAGRAMS

10. TREE DIAGRAMS  Tree Diagrams are VISUAL representations of the possible OUTCOMES in a scenario  Example: Outcomes for flipping 3 coins

11. TREE DIAGRAMS  Draw a tree diagram to represent the situation At a small ice cream parlor, you can choose from 4 flavors of ice cream, 3 toppings, and 2 syrups. Make a tree diagram to represent the possible choices you can make for an ice cream sundae.

12. FUNDAMENTAL COUNTING PRINCIPLE

13.  Use the Fundamental Counting Principle to find the number of outcomes for the situation: You want to buy the perfect tree and decorations for the holiday season. You can choose from a douglas fir tree, noble fir tree, cedar tree, or a spruce tree. You can choose from a strand of white lights, colored lights, white lights that twinkle, and colored lights that twinkle. You can choose from striped ornaments, solid ornaments, or handmade ornaments. Lastly, you can choose from 6 different tree toppers. How many ways can you choose to make the perfect tree?

14. PERMUTATIONS  Permutations are used to find the number of DIFFERENT ways to order items  ORDER MATTERS  That means that every time you flip 2 items, you create a NEW order  To solve Permutations  Use can use BLANKS  Use can use FACTORIALS (!)  You can use nPr in your calculator  n is the number of items you HAVE  r is the number of items you WANT to put in order

15. PERMUTATIONS

16.  You Try:  How many ways can you rearrange the letters in the word “papajohnspizza” to create a new word?  How many ways can 6 people choose to sit in a row that has 8 empty seats?

17. COMBINATIONS  Combinations are used to find the number of OUTCOMES that can happen in a scenario  ORDER DOES NOT MATTER  That means that even if you pick items in a different order, you still have the SAME number of items  To solve Combinations  Use nCr in your calculator  n is the number of items you HAVE  r is the number of items you WANT to select

18. COMBINATIONS

19.  You Try:  How many ways can you select 3 toys from a bin of 23 toys?  How many ways can you choose a pizza with 4 toppings if you have 21 toppings to choose from?

20. ALL DONE