You pick a marble at random. What is the probability:

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You pick a marble at random. What is the probability: Warm-Up Honors Algebra 2 5/23/19 You pick a marble at random. What is the probability: 2 5 P(purple) = P(purple or white) = P(green) = 4 5 0 5 =0

Sample Space is the set of ALL possible outcomes of an event. List the sample space, S, for each of the following: a. Tossing a coin. S = {H, T} b. Rolling a standard six-sided die. S = {1, 2, 3 ,4, 5, 6} c. Drawing a marble from a bag that contains two red, three blue and one white marble. S = {red, red, blue, blue, blue, white}

Intersection and Union of Sets The intersection of two sets (A  B) is the set of all the elements in both set A AND set B. The union of two sets (A  B) is the set of all the elements in set A OR set B. Example: Given the following sets A and B, find A  B and A  B. A = {1,3,5,7,9,11,13,15} B = {0,3,6,9,12,15} A  B = {3, 9, 15} A  B = {0, 1 , 3, 5, 6, 7, 9, 11, 12, 13, 15} Stress that intersection means AND and that union means OR

Venn Diagram is a visual representation of sets and their relationships to each other using overlapping circles. Each circle represents a different set.

Use the Venn Diagram to answer the questions below: What are the elements of set A? {1, 2, 3, 4, 6, 12} What are the elements of set B? {1, 2, 4, 8, 16} Why are 1, 2, and 4 in both sets? They are factors of Both 12 and 16

4. What is A  B? {1, 2, 4} 5. What is A  B? {1, 2, 3, 4, 6 ,8, 12, 16} Explain to students that the intersection is the overlap of the circles and the union is everything in both circles.

In a class of 60 students, 21 sign up for chorus, 29 sign up for band, and 5 take both. 15 students in the class are not enrolled in either band or chorus. 6. Put this information into a Venn Diagram. If the sample space, S, is the set of all students in the class, let students in chorus be set A and students in band be set B. 7. How many students are in A  B? 8. How many students are in A  B?

5 16 15 A  B = A  B = 45 students 15 students S. Students in the class 15 B. Students in Band 24 A. Students in Chorus 5 16 A  B = A  B = 45 students 15 students

Compliment of a Set is the set of all elements NOT in the original set. The compliment of a set A, is denoted as 𝐀 ′ or AC Example: S = {…-4, -3, -2, -1, 0, 1, 2, 3, 4,…} A = {…-4, -2, 0, 2, 4,…} If A is a subset of S, what is AC? AC = {…-3, -1, 1, 3,…} Stress that compliment means NOT

16 5 39 31 55 15 How many students are in AC? In BC? S. Students in the class 15 B. Students in Band 24 A. Students in Chorus 16 5 How many students are in AC? In BC? 10. How many students are in (A  B)C? How many students are in (A  B)C? 39 31 55 15