1. At a local college, 35.1% of students major in business, 12.3% of students major in economics, and 2.6% of students major in business and economics. What is the probability that a randomly selected student majors in business or economics?

2.At Case Western Reserve University, 48.0% of the student body are undergraduates and 52.0% of those enrolled are graduate students. 61.3% of undergraduate students participate in extracurricular activities, while only 33.3% of graduate students participate in extracurricular activities. A student who participates in extracurricular activities is randomly selected. What is the probability that the student is agraduate student? Use Baye's theorem to solve this problem.

3. There are 12 blue shirts and 7purple shirts in a drawer. Three shirts are randomly selected without replacement. What is the probability of selectingtwo purple shirts then a blue shirt?

4. A company set up a kiosk at Great Lakes Mall for several hours and asked 150 randomly selected people where they prefer to watch movies. The results follow:

	Females	Males	Total
At the theater	32	27	59
Online	15	23	38
On the television	20	22	42
"I don't watch movies"	5	6	11
Total	72	78	150

a) What is the probability that a randomly selected person is a male given that prefer watching movies online?

b) What is the probability that a randomly selected person prefers to watch movies on the television?

5. Suppose P(A) = .713, P(B) = .626, P(A|B) = .651.

a) What is P(A and B)?

b) What is P(B|A)?

6. Each player in a certain football league was rated on their current ability and their potential for improvement. The data for the 390 sampled players is summarized in the table. Potential for Improvement

Current Ability	Excellent	Good	Fair	Total
Above Average	62	71	70	203
Average	33	50	45	128
Below Average	20	28	11	59
Total	115	149	126	390

a) What is the probability that a randomly selected player has fair potential for improvement?

b) What is the probability that a randomly selected player hasaverage current ability or has good potential for improvement? (Write your answer as a fraction reduced to lowest terms. Format 0/0)

7. a) A pair of fair dice is thrown. What is the probability of rolling a value between 3and 6, inclusive?

b) What is the probability of drawing a rednumbered card when a single card is randomly drawn from a standard deck of 52 cards?

8. The Cleveland Cavaliers have a roster of 17players. The team must choose 6 of the players so they can deliver food and souvenirs to children at St. Vincent's Hospital. How many ways can 6 players be selected?

9. A professor must choose 4 of his 30students and assign them to class positions. The positions will be president, vice president, secretary, and treasurer. (No student can hold more than one position). How many ways can the positions be selected?

10. Jacob Malone must select a freshman, a sophomore, a junior, a senior, and a graduate student, to comprise a panel for the science fair. He must select the panel from a group of 8 freshmen, 6sophomores, 5juniors, 4seniors, and 10graduate students. How many ways can he select the panel?