Unit 7: Probability Lesson 1

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Presentation transcript:

Unit 7: Probability Lesson 1 Set Notation Venn Diagrams Probability Basics

The Standard: MCC9-12.S.CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

Learning Target I can use set notation and represent a sample space using a lattice or a Venn Diagram.

Vocabulary: Probability: the chance something will happen Sample Space: a set of all possible outcomes Set: contains an object or objects that are clearly identified Elements (or members): the objects in a set Union: contains all the elements in either or both sets Intersection: shows which elements sets have in common Complement: the elements in the universal set that are not included in that set Venn Diagram: a visual way to see two or more variables

Set Theory: A set s a collection of elements, such as objects or numbers. You can indicate a set by listing the elements in braces. If every element in a set also belongs to another set, then the first set is a subset of the second set. A set containing all the possible elements is called the universal set, denoted by the letter U. A set can have a complement, which includes the elements in the universal set which are not included in that set. The complement of a subset B is denoted by 𝑩 , read B bar or not B. The intersection of sets, shown by the symbol ∩, consists of only the elements that the two sets have in common. The union of sets, shown by the symbol ∪, consists of all the elements contained in either or both sets.

Example: given a six-sided die, with the sides numbered 1,2,3,4,5, and 6. Identify the universal set: Identify the subset of even numbered sides: Identify the intersection of prime and even numbers: Identify the union of the subsets – odd and prime numbers:

The Venn Diagram: 21 35 10

Reading a Venn Diagram: how many students play football and baseball? How many students play baseball? How many students play both? How may students were surveyed? football baseball