Chapter 14

According to the American Pet Products Manufacturers Association's \(2017-2018\) National Pet Owners Survey, there is a \(68 \%\) probability that a U.S. household owns a pet. If a U.S. household is randomly selected, what is the probability that it does not own a pet?

How many different 11-letter words (meaningful or not) can be formed from the letters in the word MATHEMATICS?

According to the American Pet Products Manufacturers Association's \(2017-2018\) National Pet Owners Survey, there is a \(38 \%\) probability that a U.S. household owns a cat. If a U.S. household is randomly selected, what is the probability that it does not own a cat?

An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

According to the National Science Foundation, in 2016 there was a \(17.2 \%\) probability that a doctoral degree awarded at a U.S. university was awarded in engineering. If a 2016 U.S. doctoral recipient is randomly selected, what is the probability that his or her degree was not in engineering?

An urn contains 15 red balls and 10 white balls. Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls: (a) If all 5 balls are red? (b) If 3 balls are red and 2 are white? (c) If at least 4 are red balls?

According to a 2016 Gallup survey, \(26 \%\) of U.S. adults visited a casino within the past year. If a U.S. adult is selected at random, what is the probability that he or she has not visited a casino within the past year?

The U.S. Senate has 100 members. Suppose that it is desired to place each senator on exactly 1 of 7 possible committees The first committee has 22 members, the second has \(13,\) the third has \(10,\) the fourth has \(5,\) the fifth has \(16,\) and the sixth and seventh have 17 apiece. In how many ways can these committees be formed?

According to the Girl Scouts of America, \(19 \%\) of all Girl Scout cookies sold are Samoas/Caramel ookies deLites. If a box of Girl Scout cookies is selected at random, what is the probability that it does not contain Samoas/Caramel deLites?

A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed?

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event. The golf ball is white or green.

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event. The golf ball is white or orange.

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event. The golf ball is not white.

A baseball team has 15 members. Four of the players are pitchers, and the remaining 11 members can play any position. How many different teams of 9 players can be formed?

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event. The golf ball is not green.

In the World Series the American League team ( \(A\) ) and the National League team ( \(N\) ) play until one team wins four games. If the sequence of winners is designated by letters (for example, \(\mathrm{NAAAA}\) means that the National League team won the first game and the American League won the next four), how many different sequences are possible?

On The Price Is Right, there is a game in which a bag is filled with 3 strike chips and 5 numbers. Let's say that the numbers in the bag are \(0,1,3,6,\) and \(9 .\) What is the probability of selecting a strike chip or the number \(1 ?\)

A basketball team has 6 players who play guard ( 2 of 5 starting positions). How many different teams are possible, assuming that the remaining 3 positions are filled and it is not possible to distinguish a left guard from a right guard?

On a basketball team of 12 players, 2 play only center, 3 play only guard, and the rest play forward (5 players on a team: 2 forwards, 2 guards, and 1 center). How many different teams are possible, assuming that it is not possible to distinguish a left guard from a right guard or a left forward from a right forward?

A combination lock displays 50 numbers. To open it, you turn clockwise to the first number of the "combination," then rotate counterclockwise to the second number, and then rotate clockwise to the third number. (a) How many different lock combinations are there? (b) Comment on the description of such a lock as a combination lock.

Based on a survey of annual incomes in 100 households. The following table gives the data. $$\begin{array}{l|ccccc}\text { Income } & \$ 0-24,999 & \$ 25,000-49,999 & \$ 50,000-74,999 & \$ 75,000-99,999 & \$ 100,000 \text { or more } \\\\\hline \begin{array}{l}\text { Number } \\ \text { of households }\end{array} & 22 & 23 & 17 & 12 & 26\end{array}$$ What is the probability that a household has an annual income between \(\$ 25,000\) and \(\$ 74,999,\) inclusive?

Based on a survey of annual incomes in 100 households. The following table gives the data. $$\begin{array}{l|ccccc}\text { Income } & \$ 0-24,999 & \$ 25,000-49,999 & \$ 50,000-74,999 & \$ 75,000-99,999 & \$ 100,000 \text { or more } \\\\\hline \begin{array}{l}\text { Number } \\ \text { of households }\end{array} & 22 & 23 & 17 & 12 & 26\end{array}$$ What is the probability that a household has an annual income of \(\$ 50,000\) or more?

In a survey about the number of TV sets in a house, the following probability table was constructed: $$\begin{array}{lccccc}\begin{array}{l}\text { Number } \\\\\text { of TV sets }\end{array} & 0 & 1 & 2 & 3 & 4 \text { or more } \\\\\hline \text { Probability } & 0.05 & 0.24 & 0.33 & 0.21 & 0.17\end{array}$$ Find the probability of a house having: (a) 1 or \(2 \mathrm{TV}\) sets (b) 1 or more TV sets (c) 3 or fewer TV sets (d) 3 or more TV sets (e) Fewer than \(2 \mathrm{TV}\) sets (f) Fewer than \(1 \mathrm{TV}\) set (g) \(1,2,\) or 3 TV sets (h) 2 or more TV sets

Explain the difference between a permutation and a combination. Give an example to illustrate your explanation.

Through observation, it has been determined that the probability for a given number of people waiting in line at the \(" 5\) items or less" checkout register of a supermarket is as follows: $$\begin{array}{lccccc}\begin{array}{l}\text { Number } \\\\\text { waiting in line }\end{array} & 0 & 1 & 2 & 3 & 4 \text { or more } \\\\\hline \text { Probability } & 0.10 & 0.15 & 0.20 & 0.24 & 0.31\end{array}$$ Find the probability of: (a) At most 2 people in line (b) At least 2 people in line (c) At least 1 person in line

Problems \(68-77\) are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the area of the sector of a circle of radius 4 feet and central angle \(\theta\) if the arc length subtended by \(\theta\) is 5 feet.

In a certain Algebra and Trigonometry class, there are 18 freshmen and 15 sophomores. Of the 18 freshmen, 10 are male, and of the 15 sophomores, 8 are male. Find the probability that a randomly selected student is: (a) A freshman or female (b) A sophomore or male

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. If \(f(x)=2 x-1\) and \(g(x)=x^{2}+x-2,\) find \((g \circ f)(x)\)

The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males Of the 4 females, 2 are under age \(40,\) and of the 9 males, 3 are under age \(40 .\) Find the probability that a randomly selected faculty member is: (a) Female or under age 40 (b) Male or over age 40

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Give exact values for \(\sin 75^{\circ}\) and \(\cos 15^{\circ}\)

What is the probability that at least 2 people in a group of 12 people have the same birthday? Assume that there are 365 days in a year.

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the 5 th term of the geometric sequence with first \(\operatorname{term} a_{1}=5\) and common ratio \(r=-2\)

What is the probability that at least 2 people in a group of 35 people have the same birthday? Assume that there are 365 days in a year.

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Use the binomial theorem to expand: \((x+2 y)^{5}\)

Lotto America is a multistate lottery in which 5 red balls from a drum with 52 balls and 1 star ball from a drum with 10 balls are selected. For a $$\$ 1$$ ticket, players get one chance at winning the grand prize by matching all 6 numbers. What is the probability of selecting the winning numbers on a $$\$ 1$$ play?

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Use the binomial theorem to expand: \((x+2 y)^{5}\)

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Multiply, if possible: \(\left[\begin{array}{rrr}4 & 2 & 0 \\ -1 & 3 & 1\end{array}\right]\left[\begin{array}{rr}0 & -2 \\ 3 & 1 \\ 5 & 0\end{array}\right]\)

Find the rectangular coordinates of the point whose polar coordinates are \(\left(6, \frac{2 \pi}{3}\right)\)

Solve: \(\log _{5}(x+3)=2\)

Solve the given system using matrices. $$\left\\{\begin{array}{rr}3 x+y+2 z= & 1 \\\2 x-2 y+5 z= & 5 \\\x+3 y+2 z= & -9\end{array}\right.$$

Evaluate: \(\left|\begin{array}{rrr}7 & -6 & 3 \\ -8 & 0 & 5 \\ 6 & -4 & 2\end{array}\right|\)

Simplify: \(\sqrt{108}-\sqrt{147}+\sqrt{363}\)

Find the 85 th term of the sequence \(5,12,19,26, \ldots\)

Find the area bounded by the graphs of \(y=\frac{3}{5} x+\frac{12}{5}, y=-x+4,\) and \(y=-\sqrt{16-x^{2}}\)

Find the partial fraction decomposition: \(\frac{7 x^{2}-5 x+30}{x^{3}-8}\)