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Home , Venn diagram

H. Geometry 371 – Venn / & Name______

1. Given the universal , Set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, determine the elements of the following subsets.

a) Set B = the multiples of 4 = ______b) Set F = # less than 5 = ______

c) Set P = prime #’s = ______d) Set K = even = ______

A = {1, 3, 5, 7, 9} B = {1, 5, 6, 7} C = {1, 2, 4, 6, 8, 9} 2. A B 3. A C 4. A B 5. A C

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}A = {1, 3, 4, 5, 9} B = {2, 4, 6, 7, 8} C = {1, 3, 4, 6}

6. A 7. C 8. AB 9. BC

10. Shade the indicated region of each Venn . a) Set A b) Set A  Set B (A AND B)

c c c) Set B d) Set A Set B (NOT B) (A AND NOT B)

c e) Set A  Set B f) Set B Set A (A OR B) (B OR NOT A)

c c g) (Set A Set B) h) Set B Set A NOT (A OR B) (B AND NOT A)

H. Geometry 371 Probability – Venn Diagrams/Subsets & Sample Space

11. Use the diagram to the right to answer the following questions. a) How many are in set A?

b) How many are in set B? A U 4 c) How many are in A or B? 15 d) How many are in A and B? B 3 2 C 5 e) How many are in A but not C? 10 2 15 f) How many are not in A? g) How many are in A and B and C? h) How many are in A or B or C?

19. A survey of 100 investors in the stock market was taken and the results are shown below. Set up a Venn diagram to answer the questions.

50 owned shares in IBM 40 owned shares in AT&T 45 owned shares in GE 20 owned shares in both IBM and GE 15 owned shares in both AT&T and GE 20 owned shares in both IBM and AT&T 5 owned shares in all three a) How many of the investors surveyed did not have shares in any of the three companies?

b) How many owned just IBM shares?

c) How many owned just GE shares?

d) How many owned neither IBM nor GE?

e) How many owned either IBM or AT&T but no GE?

H. Geometry 371 Probability – Venn Diagrams/Subsets & Sample Space

1. Determine the sample space by listing the elements of the sample space in set notation and then determine the number of possible outcomes in that sample space. a) Rolling an 8 sided die. b) The possible genders of the c) The factors of 12. two children in a family.

______d) A bag of marbles with 3 Red, e) The sum of two dice. f) The suits of a deck of cards 2 Green and 5 Yellow.

______g) The letters in the word, Golf. h) The digits in the number, i) Rolling a dice with sides of 13430. 1, 3, 4, 3, 3, 1.

______

2. Determine the sample space from the diagram - list the elements of the sample space in set notation. a) The numbers on the spinner. b) The marbles in the bag. c) Positions of the basketball team.

d) The text on the tiles. e) Continents on bar graph. f) cell phone providers

3. Out of 50 students, 33 are taking AP Calculus and 14 are taking AP World and not Calculus. Fill out the Venn diagram with the information and then determine how many students are not taking either of these classes?

H. Geometry 371 Probability – Venn Diagrams/Subsets & Sample Space 4. Out of 50 students, 28 are taking AP Calculus and 19 are taking AP World and 10 are taking both. Fill out the Venn diagram with the information and then determine how many students are just taking AP Calculus and Not AP World?

5. In a of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?

6. In a school of 300 students, 90 students are in the band, 185 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports?

7. A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?

8. From a survey of 100 college students, a marketing research company found that 75 students owned stereos, 45 owned cars, and 35 owned cars and stereos. a) How many students owned either a car or a stereo?

b) How many students did not own either a car or a stereo?