UNIT 8: PROBABILITY Final Exam Review

TOPICS TO INCLUDE

Sample SpaceBasic ProbabilityVenn DiagramsTree DiagramsFundamental Counting PrinciplePermutationsCombinations

SAMPLE SPACE

Sample Space is a LIST of all of the possible OUTCOMES in a scenarioExample: Write the sample space for the types of cards that can be selected in a deck of cardsA, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K

Example: List the sample space for rolling a dice1, 2, 3, 4, 5, 6

SAMPLE SPACE

Now you try:

List out the sample space: List the sample space for the colors in a bag of regular M&Ms

BASIC PROBABILITY

Probability is used a lot in a DECK OF CARDS The DENOMINATOR should always be 52Always REDUCE!

ExampleP(black card)P(card <4)

Answer: 26/52 or ½Answer: 12/52 or 3/13

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)

VENN DIAGRAMS

Venn Diagrams are a VISUAL representation used to COMPARE dataWhen filling out a Venn Diagram, always START in the MIDDLEAlways check to make sure that ALL data has been used. If not, complete the diagram with a number OUTSIDE of the circles.

VENN DIAGRAMS

The Symbol stands for INTERSECTIONIt’s the number in the MIDDLE of the diagram

The symbolstands for UNIONIt’s the SUM of the numbers INSIDE the circles

VENN DIAGRAMS

Fill out the Venn Diagram and then solve the problems that follow:

55 people were questioned at a concert. 43 people said that they like to stand during a concert. 23 people said that they like to sit during a concert. 14 people said that they like to do both.

1. Find A B2. Find A B3. How many people do not like to sit during a concert4. How many people either like to sit or stand during a concert, but not both?

TREE DIAGRAMS

Tree Diagrams are VISUAL representations of the possible OUTCOMES in a scenarioExample: Outcomes for flipping 3 coins

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.

FUNDAMENTAL COUNTING PRINCIPLEThe Fundamental Counting Principle is a SHORTCUT to a Tree Diagram. All you need to do is MULTIPLY the choices together to find out how many outcomes are possible.

Example: In how many ways can you select one dog, one gorilla, and one penguin from a collection of 7 different dogs, 6 different gorillas, and 3 different penguins? Answer: 7 6 3 = 126

FUNDAMENTAL COUNTING PRINCIPLEUse 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?

PERMUTATIONSPermutations are used to find the number of DIFFERENT ways to order itemsORDER MATTERSThat means that every time you flip 2 items, you create a NEW orderTo solve PermutationsUse can use BLANKSUse 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

PERMUTATIONS

ExampleHow many ways can you arrange the letters in the word “SNOWMAN” to make a new word?

How many ways can you put 4 books in order on a bookshelf from a selection of 10 books?

P4 = 5040

PERMUTATIONS

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?

COMBINATIONS

Combinations are used to find the number of OUTCOMES that can happen in a scenarioORDER DOES NOT MATTERThat means that even if you pick items in a different order, you still have the SAME number of itemsTo solve CombinationsUse nCr in your calculator

n is the number of items you HAVE r is the number of items you WANT to select

COMBINATIONS

Examples:How many ways can you select a group of 6 people from a class of 25 people?

25C6 = 177100

How many ways can you choose 1 math class, 1 english class, and 1 PE class if there are 5 math classes to choose from, 3 english classes to choose from, and 7 PE classes to choose from?

5C1 3C1 7C1 = 105

COMBINATIONS

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?

ALL DONE