Math 2 Probability Lesson 10.2 Types of Representations

Vocabulary Tree Diagrams Geometric Diagrams Venn Diagrams Two-way Table Disjoint Probability Joint Probability (overlapping) Conditional Probability Notation of Unions (or) Notation of Intersections (and)

Review Multiplication Principle: If an event occurs in m ways and another event occurs independently in n ways, then the two events can occur in m × n ways. Factorials: The result of multiplying a sequence of descending natural numbers (such as 4 × 3 × 2 × 1)  The symbol is "!"

Vocabulary Arranging without replacement: when you use an item in the arrangement, it is “used up” and can’t be used again. Think of arranging people in a line. Once a person is in the front of the line, he cannot also be in the back of the line at the same time. (examples: socks, demo cd) Arranging with replacement: when an item is used in one position in an arrangement, it can be used again in another position in the arrangement. Think of arranging numbers and Letters on a license plate: the previous number or letter can be used again.

Effect on Muliplication Principle of counting (Product of the # of options for each step) Arranging without replacement: Arranging 3 people in a line. Factorial Arranging with replacement: Arranging 3 numbers on a licence plate.

Your turn: Which is it (with or without replacement) for: *Assigning 3 committee members to the positions of: “Pres”, “Vice-Pres”, and “Secretary” *The total number of social security numbers with 9 digits.

Review: Theoretical Probability The probability of an event occurring: There are 4 different colored marbles in a bag (red, blue, green and yellow). What is the probability of pulling out a red one on the first try?

The probability of drawing a “king” from a deck of cards. Examples: The probability of rolling a ‘5’ using one die. The probability of drawing a “king” from a deck of cards.

Representations of Probability Geometric Diagrams Venn Diagrams Joint Probability Disjoint Probability Two-way Table Joint Probability – overlapping Conditional Probability *Don’t forget that we looked tree diagrams for an example of showing probability.

Geometric Probability: the area of each ring is given. If an arrow will randomly hit anywhere inside of the red circle, what is the probability of hitting the center blue circle?

Joint Probability: Probability of overlapping events These types of problems involve items that can be characterized more than one way: People with Blonde Hair Blonde Girls Girls Blue Chevys BLUE Cars Chevys

Examples of Joint Probability

Disjoint Probability: Probability of Mutually Exclusive Events

Examples of Disjoint Probability

Joint Probability (overlapping) Blonde Hair (3) Maria Angelica Bill Jim Amber Girls (3) (1) (2) (2) Girl, not blonde Boy, blonde Girl, blonde (1) (2) (2)

Joint Probability (overlapping) Girl, not blonde Boy, blonde Girl, blonde (1) (2) (2) 1/5, 2/5, 0/5, 2/5

Two-way Table Representation Joint Probability Maria Angelica Bill Jim Girl Blonde Amber Boy Girl total Blonde Not blonde 2 1 3 2 2 2 3 5

Two-way Table Representation Joint Probability Maria Angelica Bill Jim Girl Blonde Amber Boy Girl total Blonde Not blonde 2 1 3 2 2 2 3 5

Two-way Table Representation Joint Probability Maria Angelica Bill Jim Girl Blonde Amber Boy Girl total Blonde Not blonde 2 1 3 2 2 2 3 5

Your turn: White Cars Fords Mustang Escort Taurus Ford 500 Honda Cobalt Mazda Camaro Fiat Vibe Citroen Focus Falcon Build a two-way table for this Venn diagram. Circle the two blocks in your table that will help you find the probability of the car being a white care that is not a Ford?

Joint (overlapping) Probability Ford Non-Ford total white Not white 7 2 9 4 4 6 7 13 2/13, 4/13, 0/13, 7/13 *Joint probability uses the overall total (circled in red)

Conditional Probability Ford Non-Ford total white Not white 7 2 9 4 4 6 7 13 1/9, 2/3,7/9, 0 *Conditional probability uses the specific totals (circled in red)

Conditional Probability Ford Non-Ford total white Not white 7 2 9 4 4 6 7 13 *Conditional probability uses the notation | not a /

Notation for Probability Unions – or Intersections - and Mutually exclusive events Additive Law of Probability Multiplication Rule and Independent Events

Vocabulary Review Tree Diagrams Geometric Diagrams Venn Diagrams Two-way Table Disjoint Probability Joint Probability (overlapping) Conditional Probability Notation of Unions (or) Notation of Intersections (and)

Representations HW You have 4 problems of Data You need to make for each 2 way chart Venn Diagram Tree Chart Problem 4. Make at least 5 probability statements about the data. Use Union and Intersection at least once.

Homework 10.2 HW 10.2 Representations of Categorical Data Part 1