Question 1

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Tossing two fair coins once

Accepted Answer

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

Question 2

Choose the one alternative that best completes the statement or answers the question.
-During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 9.5 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a
Thunderstorm? Round to two decimal places, if necessary.

Accepted Answer

A)   0.91
B)   0.68
C)   0.31
D)   0.69E) A) and D)
F) A) and C)

Question 3

Solve the problem.
-In how many ways can 2 people each have different birth months?

Accepted Answer

A)   132
B)   24
C)   66
D)   144E) A) and B)
F) B) and C)

Question 4

Determine whether the following is a probability model.
-  Outcome  Probability  Red −0.21 Blue 0.27 Green 0.30 White 0.22\begin{array}{l|c}	ext { Outcome } & 	ext { Probability } \\hline 	ext { Red } & -0.21 \	ext { Blue } & 0.27 \	ext { Green } & 0.30 \	ext { White } & 0.22\end{array} Outcome  Red  Blue  Green  White ​ Probability −0.210.270.300.22​​

Accepted Answer

A)   Yes
B)   No C) A) and B)
D) undefined

Question 5

Solve the problem.
-The following data represent the marital status of females 18 years and older in a certain U.S. city.   Marital Status  Number (in thousands)   Married 308 Widowed 58 Divorced 65 Never married 114\begin{array} { l | c } 	ext { Marital Status } & 	ext { Number (in thousands)  } \\hline 	ext { Married } & 308 \	ext { Widowed } & 58 \	ext { Divorced } & 65 \	ext { Never married } & 114\end{array} Marital Status  Married  Widowed  Divorced  Never married ​ Number (in thousands)  3085865114​​  Determine the number of females 18 years old and older who are married or widowed.

Accepted Answer

A)   373,000
B)   366,000
C)   308,000
D)   431,000 E) A) and D)
F) None of the above

Question 6

Solve the problem.
-A group of 7 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Accepted Answer

A)   6
B)   7
C)   5,040
D)   720E) B) and C)
F) C) and D)

Question 7

Choose the one alternative that best completes the statement or answers the question.
-A 6-sided die is rolled. What is the probability of rolling a number less than 3?

Accepted Answer

A)    16\frac { 1 } { 6 }61​ 
B)    13\frac { 1 } { 3 }31​ 
C)    12\frac { 1 } { 2 }21​ 
D)    23\frac { 2 } { 3 }32​E) All of the above
F) A) and B)

Question 8

Solve the problem.
-A student must choose 1 of 5 mathematics electives, 1 of 7 science electives, and 1 of 7 programming electives. How many possible course selections are there?

Accepted Answer

A)   490 course selections
B)   19 course selections
C)   245 course selections
D)   35 course selectionsE) A) and B)
F) None of the above

Question 9

Solve the problem.
-If  n(B) =24,n(A∩B) =5n ( B )  = 24 , n ( A \cap B )  = 5n(B) =24,n(A∩B) =5 , and  n(A∪B) =42n ( A \cup B )  = 42n(A∪B) =42 , find  n(A) n ( A ) n(A)  .

Accepted Answer

A)   21
B)   18
C)   23
D)   25 E) A) and C)
F) A) and D)

Question 10

Find the value of the permutation.
-P(4, 0)

Accepted Answer

A)   2
B)   1
C)   48
D)   24E) All of the above
F) C) and D)

Question 11

Solve the problem.
-A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Accepted Answer

A)   1,048,576
B)   400
C)   190
D)   40E) A) and C)
F) B) and D)

Question 12

Solve the problem.
-How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Accepted Answer

A)   360
B)   4,096
C)   30
D)   15E) All of the above
F) B) and C)

Question 13

Solve the problem.
-Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a
Must?

Accepted Answer

A)   336; 210
B)   3,360; 420
C)   6,720; 840
D)   56; 35E) A) and B)
F) A) and C)

Question 14

Choose the one alternative that best completes the statement or answers the question.
-Given that  P(A) =0.56P ( A )  = 0.56P(A) =0.56  and  P(B) =0.26P ( B )  = 0.26P(B) =0.26 , find  P(A∪B) P ( A \cup B ) P(A∪B)   if  AAA  and  BBB  are mutually exclusive.

Accepted Answer

A)    0.67440.67440.6744 
B)    0.14560.14560.1456 
C)    0.820.820.82 
D)   0 E) A) and B)
F) B) and D)

Question 15

Choose the one alternative that best completes the statement or answers the question.
-How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

Accepted Answer

A)   560
B)   18
C)   56
D)   21E) All of the above
F) A) and C)

Question 16

Choose the one alternative that best completes the statement or answers the question.
-A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is red or green when one marble is drawn from the bag?

Accepted Answer

A)   6
B)    23\frac { 2 } { 3 }32​ 
C)    13\frac { 1 } { 3 }31​ 
D)    32\frac { 3 } { 2 }23​E) C) and D)
F) A) and D)

Question 17

Choose the one alternative that best completes the statement or answers the question.
-In a survey about the number of siblings of college students, the following probability table was constructed:   Number of Siblings  Probability 00.2410.3220.1930.144 or more 0.11\begin{array} { c | c } 	ext { Number of Siblings } & 	ext { Probability } \\hline 0 & 0.24 \\hline 1 & 0.32 \\hline 2 & 0.19 \\hline 3 & 0.14 \\hline 4 	ext { or more } & 0.11\end{array} Number of Siblings 01234 or more ​ Probability 0.240.320.190.140.11​​  What is the probability that a student has less than 2 siblings?

Accepted Answer

A)   0.75
B)   0.19
C)   0.25
D)   0.56 E) A) and B)
F) A) and C)

Question 18

Solve the problem.
-How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Accepted Answer

A)   36
B)   72
C)   512
D)   81E) A) and C)
F) B) and D)

Question 19

Solve the problem.
-Among a group of 80 investors, 19 owned shares of Stock A, 29 owned shares of Stock B, 40 owned shares of Stock C, 12 owned shares of both Stock A and Stock B, 9 owned shares of Stock A and Stock C, 13 owned shares
Of Stock B and Stock C, and 7 owned shares of all three. How many investors did not have shares in any of the
Three? How many owned shares of either Stock A or Stock C but not Stock B?

Accepted Answer

A)   19; 37
B)   19; 30
C)   26; 30
D)   19; 32E) A) and D)
F) B) and D)

Question 20

Solve the problem.
-List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(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 C(6, 2)  = 30
B)   ab, ac, ad, ae, bc, bd, be, cd, ce, cf, de, df C(6, 2)  = 12
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, fa, fb, fc, fd, fe, ffC(6, 2)  = 36
D)   ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef C(6, 2)  = 15E) B) and C)
F) A) and B)

Exam 12: Counting and Probability

Solve the problem. -A group of 7 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Correct Answer
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Solve the problem. -How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Correct Answer
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Solve the problem. -If $n ( B ) = 24 , n ( A \cap B ) = 5$ , and $n ( A \cup B ) = 42$ , find $n ( A )$ .

Correct Answer
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Solve the problem. -In how many ways can 2 people each have different birth months?

Correct Answer
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Solve the problem. -How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Correct Answer
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Solve the problem. -Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a Must?

Correct Answer
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Determine whether the following is a probability model. - $\begin{array}{l|c}\text { Outcome } & \text { Probability } \\\hline \text { Red } & -0.21 \\\text { Blue } & 0.27 \\\text { Green } & 0.30 \\\text { White } & 0.22\end{array}$

Correct Answer
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Find the value of the permutation. -P(4, 0)

Correct Answer
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Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is red or green when one marble is drawn from the bag?

Correct Answer
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Correct Answer
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Solve the problem. -A student must choose 1 of 5 mathematics electives, 1 of 7 science electives, and 1 of 7 programming electives. How many possible course selections are there?

Correct Answer
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Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Correct Answer
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Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -A 6-sided die is rolled. What is the probability of rolling a number less than 3?

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -Given that $P ( A ) = 0.56$ and $P ( B ) = 0.26$ , find $P ( A \cup B )$ if $A$ and $B$ are mutually exclusive.

Correct Answer
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Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Tossing two fair coins once

Correct Answer
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Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

Correct Answer
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Solve the problem. -List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2) ?

Correct Answer
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Exam 12: Counting and Probability

Solve the problem. -A group of 7 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Correct AnswerverifiedShow Answer

Solve the problem. -How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Correct AnswerverifiedShow Answer

Solve the problem. -If n(B) =24,n(A∩B) =5n ( B ) = 24 , n ( A \cap B ) = 5n(B) =24,n(A∩B) =5 , and n(A∪B) =42n ( A \cup B ) = 42n(A∪B) =42 , find n(A) n ( A ) n(A) .

Correct AnswerverifiedShow Answer

Solve the problem. -In how many ways can 2 people each have different birth months?

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Solve the problem. -How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Correct AnswerverifiedShow Answer

Solve the problem. -Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a Must?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the value of the permutation. -P(4, 0)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. -A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is red or green when one marble is drawn from the bag?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem. -A student must choose 1 of 5 mathematics electives, 1 of 7 science electives, and 1 of 7 programming electives. How many possible course selections are there?

Correct AnswerverifiedShow Answer

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. -A 6-sided die is rolled. What is the probability of rolling a number less than 3?

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. -Given that P(A) =0.56P ( A ) = 0.56P(A) =0.56 and P(B) =0.26P ( B ) = 0.26P(B) =0.26 , find P(A∪B) P ( A \cup B ) P(A∪B) if AAA and BBB are mutually exclusive.

Correct AnswerverifiedShow Answer

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Tossing two fair coins once

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. -How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

Correct AnswerverifiedShow Answer

Solve the problem. -List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2) ?

Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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Solve the problem. -If $n ( B ) = 24 , n ( A \cap B ) = 5$ , and $n ( A \cup B ) = 42$ , find $n ( A )$ .

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Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -Given that $P ( A ) = 0.56$ and $P ( B ) = 0.26$ , find $P ( A \cup B )$ if $A$ and $B$ are mutually exclusive.

Correct Answer
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Correct Answer
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