1. Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $6. If you roll a one, two, or three, you pay $5.

(a)What are you ultimately interested in here (the value of the roll or the money you win)?

• A. the number rolled
• B. the number of times a six is rolled
• C. the amount of winnings
• D. the type of die

(b)In words, define the Random VariableX.

• A. the amount of numbers that can be rolled
• B. the amount of winnings
• C. the probability of rolling a four
• D. the amount of money made by rolling a six

(c)List the values thatXmay take on.

• A. $5, $6, $10
• B. 1, 2, 3, 4, 5, 6
• C. 4, 5, 6
• D. $5, $6, $10

(d)Construct a PDF. (Enter your answers forP(X=x) as fractions. Round your answers forxP(X=x) to two decimal places.)

	X	P(X=x)	xP(X=x)
6
4 or 5
1, 2, or 3

(e) Over the long run of playing this game, what are your expected average winnings per game? (Round your answer to two decimal places.) $ ______

(f) Based on numerical values, should you take the deal?

• A. Yes, you should take the deal because the expected value is positive.
• B. No, you should not take the deal because the expected value is negative.

2. Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.

x	P(x)	xP(x)
0	0.15
1	0.25
2	0.30
3
4	0.10
5	0.05
6 (or more)	0.05

(a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.)

__________

(b) In words, what does the expected value in this example represent? A. the number of children adults in the country have

B. the number of children married adults in the country have

C. the average number of children adults in the country have

D. the average number of children married adults in the country have

(c) Find the expected value. (Enter your answer to two decimal place.) _____ children

(d) Is it more likely that a married adult will have two to three children or four to six children? How do you know? A. it is more likely to have four to six children, with p = 0.8

B. it is more likely to have two to three children, with p = 0.3

C. it is more likely to have two to three children, with p = 0.4

D. it is more likely to have four to six children, with p = 0.1

E. it is more likely to have four to six children, with p = 0.2

3. A school newspaper reporter decides to randomly survey 17 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

(a) In words, define the Random Variable X.

A. the school newspaper

B. the number of students in the school

C. the number of students that will attend Tet

D. the types of festivities offered at the school

(b) List the values that X may take on.

A. X = 1, 2, 3, ..., 17

B. X = 0, 1, 2, ..., 17

C. X = 1, 2, 3, ..., 23

D. X = 0, 1, 2, ..., 23

(c) Give the distribution ofX. X~ ___ ( ___ , ___ )

(d) How many of the 17 students do we expect to attend the festivities? (Round your answer to the nearest whole number.) ____ student(s)

(e) Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)

(f) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

4. Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 80 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school.

(a) In words, define the Random Variable X.

A. the number of seniors that participated in after-school sports all four years of high school

B. the number of seniors who stayed after school for any activity all four years of high school

C. the number of students that participate in after-school sports

D. the number of seniors that participated in after-school sports their senior year

(b) List the values that X may take on.

A. X = 0, 1, 2, 3, 4, 5, 6, 7, 8

B. X = 0, 1, 2, ..., 78, 79, 80

C. X = 1, 2, 3, 4, 5, 6, 7, 8

D. X = 1, 2, 3, ..., 78, 79, 80

(c) Give the distribution ofX. X~ ___ ( ___ , ___ )

(d) How many seniors are expected to have participated in after-school sports all four years of high school? (Round your answer to the nearest whole number.) _____ seniors

(e) Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school?

A. Yes. The probability that none of the seniors participated in after-school sports all four years of high school is low (less than 5%).

B. No. The probability that none of the seniors participated in after-school sports all four years of high school is high (more than 10%).

(f) Based upon numerical values, is it more likely that 5 or that 6 of the seniors participated in after-school sports all four years of high school?

A. 5 seniors

B. 6 seniors

5. A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 27%. We are interested in the number of dealerships she must call.

(a) In words, define the Random Variable X.

A. the number of used red Miatas that a dealership carries

B. all car dealerships in one town

C. the cost of a used red Miatathe number of dealerships

D. the consumer must call until she finds a used red Miata

(b) List the values that X may take on.

A. X = 0, 1, 2, ...

B. X = 1, 2, 3, ..., 98, 99, 100

C. X = 1, 2, 3, ...

D. X = 1, 2, 3, ..., 26, 27

(c) Give the distribution ofX. X~ ___ ( ___ , ___ )

(d) On average, how many dealerships would we expect her to have to call until she finds one that has the car? (Round your answer to the nearest whole number.) ______ dealerships

(e) Find the probability that she must call at most 9 dealerships. (Round your answer to four decimal places.)

(f) Find the probability that she must call 5 or 6 dealerships. (Round your answer to four decimal places.)