Question 1

Determine whether the following is a probability model.
-

Accepted Answer

A) Yes 
B) No

Question 2

Find the value of the permutation.
-P(5, 1)

Accepted Answer

A) 5 
B) 120 
C) 1 
D) 24

Question 3

Solve the problem.
-A student must choose 1 of 4 mathematics electives, 1 of 6 science electives, and 1 of 9 programmingelectives. How many possible course selections are there?

Accepted Answer

A) 216 course selections 
B) 19 course selections 
C) 24 course selections 
D) 432 course selections

Question 4

Determine whether the following is a probability model.
-

Accepted Answer

A) Yes 
B) No

Question 5

Solve the problem.
-The psychology lab at a college is staffed by 9 male doctoral students, 8 female doctoral students, 10 maleundergraduates, and 14 female undergraduates. If a person is selected at random from the group, find theprobability that the selected person is an undergraduate or a female.

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Solve the problem.
-List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

Accepted Answer

A) 123, 124, 134, 234 C(4, 3)= 4 
B) 123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431 C(4, 3)= 24 
C) 123, 124, 134, 234, 321, 432 C(4, 3)= 6 
D) 111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334,
341, 342, 343, 344, 411, 412, 413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444
C(4, 3)= 64

Question 7

Solve the problem.
-The table below shows the results of a consumer survey of annual incomes in 100 households.  What is the probability that a household has an annual income between $15,000 and $44,999 inclusive?

Accepted Answer

A) 0.77 
B) 0.28 
C) 0.49 
D) 0.48

Question 8

Solve the problem.
-An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 6 of themultiple-choice questions and 2 of the essay questions, in how many ways can the questions be chosen?

Accepted Answer

A) 1260 
B) 648 
C) 261,273,600 
D) 1,814,400

Question 9

Solve the problem.
-What is the probability that at least 2 people have the same birth month in a group of 6 people?

Accepted Answer

A) 0.777 
B) 0.223 
C) 0.788 
D) 0.212

Question 10

Solve the problem.
-List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without repetition.What is P(6, 2)?

Accepted Answer

A) ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe P(6, 2)= 30 
B) ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2)= 15 
C) aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fb, fc, fd, fe, ff
P(6, 2)= 36 
D) ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef P(6, 2)= 25

Question 11

Solve the problem.
-How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can beused more than once.

Accepted Answer

A) 90 
B) 1,814,400 
C) 45 
D) 3,628,800

Question 12

Solve the problem.
-Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely.Compute the probability of the event E = {1, 2, 4, 5, 7, 9, 10}.

Accepted Answer

A)   
B)   
C)   
D) 7

Question 13

Solve the problem.
-How many arrangements of answers are possible in a multiple-choice test with 9 questions, each of whichhas 3 possible answers?

Accepted Answer

A) 19,683 
B) 60,480 
C) 84 
D) 504

Question 14

Solve the problem.
-A spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on aneven number or a multiple of 3?

Accepted Answer

A)   
B) 1 
C)   
D) 15

Question 15

Solve the problem.
-In a survey about the number of siblings of college students, the following probability table was constructed  What is the probability that a student 3 or more siblings?

Accepted Answer

A) 0.25 
B) 0.12 
C) 0.13 
D) 0.75

Question 16

Solve the problem.
-A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an evennumber when one ball is drawn from the bag?

Accepted Answer

A)   
B)   
C)   
D) 7

Question 17

Solve the problem.
-Find the probability of having 4 girls in a 4-child family.

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Rolling a 6-sided fair die twice

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Solve the problem.
-How many different license plates can be made using 2 letters followed by 3 digits selected from the digits0 through 9, if digits may be repeated but letters may not be repeated?

Accepted Answer

A) 650,000 
B) 128.968254 
C) 486,720 
D) 676,000

Question 20

Solve the problem.
-Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely.Compute the probability of the event E: ʺa number divisible by 3ʺ.

Accepted Answer

A)   
B)   
C)   
D) 3

Exam 10: Counting and Probability

Determine whether the following is a probability model. -

Find the value of the permutation. -P(5, 1)

Solve the problem. -A student must choose 1 of 4 mathematics electives, 1 of 6 science electives, and 1 of 9 programmingelectives. How many possible course selections are there?

Determine whether the following is a probability model. -

Solve the problem. -The psychology lab at a college is staffed by 9 male doctoral students, 8 female doctoral students, 10 maleundergraduates, and 14 female undergraduates. If a person is selected at random from the group, find theprobability that the selected person is an undergraduate or a female.

Solve the problem. -List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3) ?

Solve the problem. -The table below shows the results of a consumer survey of annual incomes in 100 households. What is the probability that a household has an annual income between $15,000 and $44,999 inclusive?

Solve the problem. -An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 6 of themultiple-choice questions and 2 of the essay questions, in how many ways can the questions be chosen?

Solve the problem. -What is the probability that at least 2 people have the same birth month in a group of 6 people?

Solve the problem. -List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without repetition.What is P(6, 2) ?

Solve the problem. -How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can beused more than once.

Solve the problem. -Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely.Compute the probability of the event E = {1, 2, 4, 5, 7, 9, 10}.

Solve the problem. -How many arrangements of answers are possible in a multiple-choice test with 9 questions, each of whichhas 3 possible answers?

Solve the problem. -A spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on aneven number or a multiple of 3?

Solve the problem. -In a survey about the number of siblings of college students, the following probability table was constructed What is the probability that a student 3 or more siblings?

Solve the problem. -A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an evennumber when one ball is drawn from the bag?

Solve the problem. -Find the probability of having 4 girls in a 4-child family.

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Rolling a 6-sided fair die twice

Solve the problem. -How many different license plates can be made using 2 letters followed by 3 digits selected from the digits0 through 9, if digits may be repeated but letters may not be repeated?

Solve the problem. -Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely.Compute the probability of the event E: ʺa number divisible by 3ʺ.