Geometry Unit 12 Note Sheets 2016

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Set Theory and Sample Space Notes Sheet You will see that set theory is useful in calculating probabilities. A set is a well-defined collection of distinct objects. Each object in a set is called an element of the set. A set may be specified by writing its elements in braces. For example, the set S of prime numbers less than 10 may be written as S = {2, 3, 5, 7}. The number of elements in a set S may be written as n(S). For the set S of prime numbers less than 10, n(S) = 4. The set with no elements is the empty set and is denoted by Ø or { }. The set of all elements under consideration is the universal set and is denoted by U. The following terms describe how sets are related to each other.

Discuss: For any set A, what is A ∩ Ø? Explain. __________________________________________________________________________________________

__________________________________________________________________________________________

Vocabulary: Sample Space – set of all possible outcomes

Tree Diagram – a diagram showing all possible outcomes of an event Guided Practice Represent the sample space for this experiment by making an organized list, a table, and a tree diagram.

1. A coin is tossed twice. Your Turn

2. Brooke could take a summer job in California or Arizona at a hotel or a bed-and-breakfast.

For any set A the intersection of A and the empty set is the emptyset

, because if there is nothing in a set it will have nothing in common .

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Geometry Unit 12 Note Sheets 2016

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Guided Practice 3. To take a hamburger order, Anthony asks each customer the questions from the script:

x What size burger would you like: kid’s, regular, or large? x Would you like cheese on that? x Would you like tomato and/or pickles?

Draw a tree diagram to represent the sample space for hamburger orders.

Fundamental Counting Principle

The number of possible outcomes in a sample space can be found by multiplying the number of possible outcomes from each stage or event.

Guided Practice 4. Esmeralda has selected a size and overall style for her class ring. Now she must choose from the rind

options shown. How many different rings could Esmeralda create in her chosen style and size? Your Turn

5. New cars are available with a wide selection of options for the consumer. One options is shown from each category shown. How many different cars could a consumer create in the chosen make and model?

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