1. Math 2 Probability Lesson 10.2
Types of Representations

2. 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)

3. 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 "!"

4. 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.

5. 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.

6. 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.

7. 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?

8. 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.

9. 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.

10. 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?

11. 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

12. Examples of Joint Probability

13. Disjoint Probability: Probability of Mutually Exclusive Events

14. Examples of Disjoint Probability

15. 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)

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

17. 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

18. 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

19. 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

20. 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?

21. 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)

22. 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)

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

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

29. 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)

30. 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.

31. Homework 10.2 HW 10.2 Representations of Categorical Data Part 1