Question 1

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, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2) = 15 
B)  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 
C)  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 
D)  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, ff
P(6, 2) = 36 
A)  ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2) = 15 
B)  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 
C)  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 
D)  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, ff
P(6, 2) = 36

Question 2

Determine whether the following is a probability model.
-$\begin{array}{l|c}
\text { Outcome } & \text { Probability } \
\hline \text { Golfing } & 0.13 \
\text { Skiing } & 0.21 \
\text { Swimming } & 0.12 \
\text { Biking } & 0.28 \
\text { Hiking } & 0.26
\end{array}$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4, and Spinner II has 4 sections of equal area, labeled Red,
Yellow, Green, and Blue. Spin Spinner I and then spin Spinner II.
What is the probability of getting a 1 or 3 followed by Red?

Accepted Answer

@#LAT-DLM& Red, 1 Yellow, 1 Green, 1 Blue, 2 Red,

Question 4

Solve the problem.
-?

Accepted Answer

A)  123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 P(4, 3) = 24 
B)  123, 124, 132, 142, 143, 213, 214, 231, 241, 243, 312, 314, 321, 341, 342, 412, 413, 421, 423, 431 P(4, 3) = 20 
C)  123, 124, 134, 234 P(4, 3) = 4 
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
P(4, 3) = 64 
A)  123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 P(4, 3) = 24 
B)  123, 124, 132, 142, 143, 213, 214, 231, 241, 243, 312, 314, 321, 341, 342, 412, 413, 421, 423, 431 P(4, 3) = 20 
C)  123, 124, 134, 234 P(4, 3) = 4 
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
P(4, 3) = 64

Question 5

Choose the one alternative that best completes the statement or answers the question.
-In the city of Gloomville, the probability of rain on New Year's Day is 65%. What is the probability that next New Year's Day it will not rain in Gloomville?

Accepted Answer

A)  35% 
B)  -65% 
C)  42.25% 
D)  65% 
A)  35% 
B)  -65% 
C)  42.25% 
D)  65%

Question 6

Choose the one alternative that best completes the statement or answers the question.
-The faculty at a college consists of 116 full-time teachers and 50 part-time teachers. Of the 116 full-time teachers, 57 are female. Of the 50 part-time teachers, 27 are female. Find the probability that a randomly
Selected teacher is male or works part-time.

Accepted Answer

A)  $\frac { 109 } { 166 }$ 
B)  $\frac { 43 } { 83 }$ 
C)  $\frac { 66 } { 83 }$ 
D)  $\frac { 23 } { 166 }$ 
A)  $\frac { 109 } { 166 }$ 
B)  $\frac { 43 } { 83 }$ 
C)  $\frac { 66 } { 83 }$ 
D)  $\frac { 23 } { 166 }$

Question 7

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: $$\begin{array} { c | c } 
\text { Number of Siblings } & \text { Probability } \
\hline 0 & 0.27 \
\hline 1 & 0.33 \
\hline 2 & 0.17 \
\hline 3 & 0.10 \
\hline 4 \text { or more } & 0.13
\end{array}$$ What is the probability that a student has at least 2 siblings?

Accepted Answer

A)  0.6 
B)  0.23 
C)  0.4 
D)  0.77 
A)  0.6 
B)  0.23 
C)  0.4 
D)  0.77

Question 8

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-A die is weighted so that an even-numbered face is three times as likely to occur as an odd-numbered face.
What probability should be assigned to each face?

Accepted Answer

The faces numbered 1, 3, 5 wil

Question 9

Choose the one alternative that best completes the statement or answers the question.
-A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or a 13?

Accepted Answer

A)  $\frac { 9 } { 10 }$ 
B)  $\frac { 10 } { 19 }$ 
C)  $\frac { 9 } { 19 }$ 
D)  $\frac { 8 } { 19 }$ 
A)  $\frac { 9 } { 10 }$ 
B)  $\frac { 10 } { 19 }$ 
C)  $\frac { 9 } { 19 }$ 
D)  $\frac { 8 } { 19 }$

Question 10

Solve the problem.
-If $n ( A ) = 40 , n ( B ) = 33$, and $n ( A \cap B ) = 10$, find $n ( A \cup B )$.

Accepted Answer

A)  83 
B)  63 
C)  53 
D)  73 
A)  83 
B)  63 
C)  53 
D)  73

Question 11

Solve the problem.
-How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 5 possible answers?

Accepted Answer

A)  78,125 
B)  21 
C)  2,520 
D)  42 
A)  78,125 
B)  21 
C)  2,520 
D)  42

Question 12

Choose the one alternative that best completes the statement or answers the question.
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 3?

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 17 } { 18 }$ 
C)  2 
D)  $\frac { 1 } { 18 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 17 } { 18 }$ 
C)  2 
D)  $\frac { 1 } { 18 }$

Question 13

Solve the problem.
-In how many ways can 12 people be lined up?

Accepted Answer

A)  12 
B)  479,001,600 
C)  239,500,800 
D)  1 
A)  12 
B)  479,001,600 
C)  239,500,800 
D)  1

Question 14

Write down all the subsets of the given set.
-$\{ a \}$

Accepted Answer

A)  $\varnothing$, \{a\} 
B)  $a$ 
C)  $\{ a , b \}$ 
D)  $\{ a \}$ 
A)  $\varnothing$, \{a\} 
B)  $a$ 
C)  $\{ a , b \}$ 
D)  $\{ a \}$

Question 15

Find the value of the permutation.
-P(11, 4)

Accepted Answer

A)  1,663,200 
B)  10,080 
C)  7,920 
D)  3,960 
A)  1,663,200 
B)  10,080 
C)  7,920 
D)  3,960

Question 16

Solve the problem.
-How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?

Accepted Answer

A)  17,576,000 
B)  36 
C)  260 
D)  9 
A)  17,576,000 
B)  36 
C)  260 
D)  9

Question 17

Solve the problem.
-Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Accepted Answer

A)  320 possible outfits 
B)  18 possible outfits 
C)  160 possible outfits 
D)  40 possible outfits 
A)  320 possible outfits 
B)  18 possible outfits 
C)  160 possible outfits 
D)  40 possible outfits

Question 18

Use the information given in the figure.
- 
How many are in $\mathrm { A }$ and $\mathrm { B }$ and $\mathrm { C }$ ?

Accepted Answer

A)  62 
B)  3 
C)  8 
D)  70 
A)  62 
B)  3 
C)  8 
D)  70

Question 19

Solve the problem.
-If $n ( A ) = 37 , n ( B ) = 52$, and $n ( A \cup B ) = 70$, find $n ( A \cap B )$.

Accepted Answer

A)  89 
B)  51 
C)  19 
D)  38 
A)  89 
B)  51 
C)  19 
D)  38

Question 20

Use the information given in the figure.
- 
How many are not in C?

Accepted Answer

A)  42 
B)  50 
C)  39 
D)  43 
A)  42 
B)  50 
C)  39 
D)  43

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)?

Determine whether the following is a probability model. - Outcome Probability Golfing 0.13 Skiing 0.21 Swimming 0.12 Biking 0.28 Hiking 0.26

Solve the problem. -?

Choose the one alternative that best completes the statement or answers the question. -In the city of Gloomville, the probability of rain on New Year's Day is 65%. What is the probability that next New Year's Day it will not rain in Gloomville?

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -A die is weighted so that an even-numbered face is three times as likely to occur as an odd-numbered face. What probability should be assigned to each face?

Choose the one alternative that best completes the statement or answers the question. -A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or a 13?

Solve the problem. -If $n ( A ) = 40 , n ( B ) = 33$ , and $n ( A \cap B ) = 10$ , find $n ( A \cup B )$ .

Solve the problem. -How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 5 possible answers?

Choose the one alternative that best completes the statement or answers the question. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 3?

Solve the problem. -In how many ways can 12 people be lined up?

Write down all the subsets of the given set. - $\{ a \}$

Find the value of the permutation. -P(11, 4)

Solve the problem. -How many different license plates can be made using 3 letters followed by 3 digits selected from the digits 0 through 9, if letters and digits may be repeated?

Solve the problem. -Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Use the information given in the figure. - $Use the information given in the figure. - How many are in \mathrm { A } and \mathrm { B } and \mathrm { C } ?$ How many are in $\mathrm { A }$ and $\mathrm { B }$ and $\mathrm { C }$ ?

Solve the problem. -If $n ( A ) = 37 , n ( B ) = 52$ , and $n ( A \cup B ) = 70$ , find $n ( A \cap B )$ .

Use the information given in the figure. - How many are not in C?

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 12: Counting and Probability