PROBABILITY AND SET ASSIGNMENT

Consider the counting numbers {1,2,3,4,5,6,7,8,9}. Let A={1,3,5,7,9}, B={2,4,6,8}, C={3,5}, D={2,4,6,8}

a) Find A union B. {A∪B}

b) Find A intersect B. {A∩B}

c) Find A complement. {A’}

d) Find {B∩C}

3)  A poll was passed out to 100 students. The poll contained 3 questions.

i) Do you own an ipad?

ii) Do you own a laptop?

ii) Do you own an ipad and a laptop?

The results of the poll are in the table. Answer the questions below using a Venn Diagram.

 a) How many students own an ipad but do not own a laptop?

b) How many students own a laptop but do not own an ipad?

c) How many own an ipad or a laptop?

d)) How many own neither an ipad nor a laptop?

e) How many do not own an ipad?

4)  A survey of students at a film school revealed the following information.

51 like animated films

49 like comedy films

60 like dramatic films

34 like animated and comedy

32 like comedy and dramatic

36 like animated and dramatic

24 like all three types

1 does not like any of the three types.

Answer the questions on the using a 3-Set Venn Diagram

a) How many like only one of the three types of film?

b) How many like animated and comedy but not dramatic?

c) How many like animated and dramatic but not comedy?

d) How many like either animated, dramatic or comedy?

e) How many like either dramatic or comedy?

f) How many like dramatic and comedy?

g) How many students were surveyed?

h) How many do not like animated

5) A marketing survey of 1,000 commuters found that 600 answered listen to the news, 500 listen to music, and 300 listen to both.  Let N = set of commuters in the sample who listen to news and M = set of commuters in the sample who listen to music. Fill out a two-set Venn diagram and give the number in each of the sets below.

a) N∩M

b) N’∩M

c) N∩M’

d) N’∩M’

e) N∪M

All of the students in Mrs. Smith’s classes belong to the Chorus, Band and/or Orchestra as shown in the Venn diagram at the right. If one student is chosen at random, what is the probability that the student belongs to the Chorus and the Band? Choose:

2. All of the students in Mrs. Smith’s classes belong to the Chorus, Band and/or Orchestra as shown in the Venn diagram at the right. If one student is chosen at random, what is the probability that the student belongs to the Chorus but not the Orchestra? Choose:

3. What of the following choices can be illustrated by the Venn diagram at the right? Choose:

4. An experiment is setup to first roll a die, followed by spinning a spinner. As shown, the die is a six-sided die and the spinner has four equal divisions labeled 1, 2, 3 and 4. Set A will contain all possibilities of the die rolling an even number and the spinner showing 4. Set B will contain all possibilities of the die and the spinner showing the same value. Find the probability of an outcome belonging to set A but not in set B.

5.	Given the Universal set to be integers 1 through 10. Set A = integers that are multiples of 3. Set B = even integers. Use the Venn diagram to decide the value of the following probabilities:
	a) P(A) b) P(A∩B) c) P(B)C d) P(A∪B) e) P(A∩B)C

6. The freshman class has a population of 160 students. The number of freshman that play in the band is 54. The number of freshman that belong to a sports team is 90. If the probability that a student participates in the band or sports is 120/160, what is the probability that a student belongs to both the band and a sports team?

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

8. Two six-sided die are rolled. Considering all possible outcomes, what is the probability that the two rolled numbers have a product that is odd?

9. In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. What is the probability that a student in the class is not enrolled in either Chorus or Band?