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Question : The table shows, for some particular year a listing of several income : 2151687

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth.

1) $5,000 - $9,999

A) 0.01

B) 0.02

C) 0.05

D) 0.03

2) $50,000 and over

A) 0.24

B) 0.25

C) 0.28

D) 0.22

3) $0 - $4,999

A) 0.02

B) 0.05

C) 0.03

D) 0.01

4) $15,000 - $19,999

A) 0.08

B) 0.04

C) 0.05

D) 0.07

5) $40,000 - $49,999

A) 0.17

B) 0.22

C) 0.21

D) 0.25

6) $20,000 - $24,999

A) 0.11

B) 0.06

C) 0.07

D) 0.08

7) $10,000 - $14,999

A) 0.05

B) 0.03

C) 0.06

D) 0.02

8) $35,000 - $39,999

A) 0.13

B) 0.11

C) 0.09

D) 0.15

9) $25,000 - $29,999

A) 0.07

B) 0.13

C) 0.09

D) 0.14

10) $30,000 - $39,999

A) 0.13

B) 0.03

C) 0.14

D) 0.26

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

11) To find P(A|B) using Bayes' theorem, what conditional probability occurs in the numerator?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

12) Given that a student correctly uses the following form of Bayes' theorem, P(R1|T) = (P(T|R_{1})P(R_{1})/P(T|R_{1})P(R_{1}) + P(T|R_{2})P(R_{2}) + P(T|R_{3})P(R_{3})), make a precise statement about the value of P(R1∪R2∪R3).

A) 0≤P≤1

B) P = 0

C) P =1

D) 0<P<1

13) Given that a student correctly uses the following form of Bayes' theorem, P(R1|T) = (P(T|R_{1})P(R_{1})/P(T|R_{1})P(R_{1}) + P(T|R_{2})P(R_{2}) + P(T|R_{3})P(R_{3})), make a precise statement about the value of P(R1∩R2∩R3).

A) 0<P<1

B) 0P≤1

C) P = 1

D) P = 0

14) Is P(R'|T) = (P(R')⋅P(T|R')/P(R)⋅P(T|R) + P(R')⋅P(T|R')) a valid alternative form of Bayes' theorem (special case)?

A) Yes

B) No

15) In using the following form of Bayes' theorem, P(R|T) = (P(T|R)P(R)/P(T|R)P(R) + P(T|R')P(R')), can P(T), if it is known, be substituted for the entire denominator?

A) No

B) Yes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

16) Assume that the events A_{1}, A_{2}, . . . , An are mutually exclusive events whose union is the sample space, and that B is an event that has occurred. Use Bayes' theorem to write an equation for P(A_{1}|B).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

17) Can an event E for a sample space S contain an outcome that is not in S?

A) No

B) Yes

18) Assume that E and F are events. Must the union of E and F also be an event? Must the intersection of E and F also be an event?

A) Both the union and the intersection must be events.

B) Only the union must be an event.

C) Neither the union nor the intersection must be an event.

D) Only the intersection must be an event.

19) A sample space S is a set of 7 outcomes. What is the least number of outcomes that an event defined for S can have?

A) 1

B) 0

C) 5040

D) 7

20) A sample space S is a set of 5 outcomes. What is the most distinct events that S can have?

A) 32

B) 1

C) 5

D) 120

21) An experiment consists of tossing a fair coin 4 times. Is it possible to have an outcome with exactly one head and exactly one tail?

A) Yes

B) No

22) If A and B are outcomes for the same sample space S, must A'∪B' be an event of S?

A) Yes

B) No

23) Two candidates for a sample space, S_{1} and S_{2}, are proposed. S_{1} = {HH, HT, TH, TT}, and S_{2} = {HH, TT, one H and one T}. Is S_{1} acceptable? Is S_{2} acceptable?

A) Only S_{2} is acceptable.

B) Both S_{1} and S_{2} are acceptable.

C) Neither S_{1} nor S_{2} is acceptable.

D) Only S_{1} is acceptable.