22.1 Probability and Set Theory ACTIVATE PRIOR KNOWLEDGE

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Presentation transcript:

22.1 Probability and Set Theory ACTIVATE PRIOR KNOWLEDGE Name:___________________________ Period:________ Lesson_1 22.1 Probability and Set Theory 1. Write each statement in set notation. Use the descriptions of the sets to the right to complete each statement. Draw a Venn Diagram to Organize the Sets A ⋂ B = { } A ∪ B = { } 2. Write each statement in set notation. Use the descriptions of the sets to the right to complete each statement. Draw a Venn Diagram to Organize the Sets A ⋂ B = { } A ∪ B = { } Remember the Concept Venn Diagrams: Shows logical relations between a collection of sets. Intersection: A ∩ B Each element is in both set A and set B. Find where the sets overlap. Union: A ∪ B All elements in set A or set B. Join together all of the elements in both sets. ACTIVATE PRIOR KNOWLEDGE Make the Connection Students you already know what is a set and subset. Now we are going to use that information to find probabilities. Note: Venn diagram can make it easier to identify the sets. A set is a collection of distinct objects. Each object in a set is called an element of the set. A set is often denoted by writing the elements in braces. The set with no elements is the empty set, denoted by ⌀ or { }. The set of all elements under is the universal set, denoted by U. Identifying the number of elements in a set is important for calculating probabilities.

Name the type of set and find the element(s)? CFU: Whiteboard Remember the Concept Intersection: A ∩ B Each element is in both set A and set B. Find where the sets overlap. Union: A ∪ B All elements in set A or set B. Join together all of the elements in both sets. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {1, 2, 3, 4, 6, 12} B = {2, 4, 6, 8, 10, 12} C = {1, 3, 5, 7, 9, 11} D = {2, 4, 6} Working with Sets: Answer each question (WB). What is A ⋂ B ? What is A ⋃ B ? What is A ⋃ C ? What is A ⋂ D ? What is B ⋂ C ? Steps to find sets 1 Identify the definition of the notation. CFU How did I/you identify the definition of the notation? 2 Apply the definition by drawing a Venn Diagram. CFU How did I/you apply the definitions by drawing a Venn Diagram? 3 Find the elements, write it on set notation. CFU How did I/you find the elements in set notation? SKILL DEVELOPMENT The complement (A’ or ) of a set of A refers to elements not in A. (Opposite)

Find the complement of A: CFU: Whiteboard To determine the complement of set A, first identify the elements of set A and universal set U separately, then identify all the elements in the universal set that are not in set A. SKILL DEVELOPMENT Homework and Practice GUIDED PRACTICE

10. Use the sets below to create Venn Diagram to the right: Homework and Practice 10. Use the sets below to create Venn Diagram to the right: GUIDED PRACTICE Remember the Concept Venn Diagrams: Shows logical relations between a collection of sets. Intersection: A ∩ B Each element is in both set A and set B. Find where the sets overlap. Union: A ∪ B All elements in set A or set B. Join together all of the elements in both sets.

Word Bank Element Universal Set Complement Subset Intersection Union Theoretical Probability What did you learn about how to describe subsets, unions, intersections, and complements of probability? SUMMARY CLOSURE Today, I learned how to _________________________________________________________________________________.