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All Textbook Solutions for Precalculus
54PE55PE56PE57PE58PEa. Write the sequence corresponding to the sum of the numbers in each row of Pascal's triangle for the first nine rows. b. Let n represent the row number in Pascal’s triangle. Write a formula for the nth term of the sequence representing the sum of the numbers in row n .60PE61PE62PE63PE64PE65PEUsing techniques from calculus, we can show that 1+xn=1+nx+nn1x22!+nn1n23!x3+ , for x1 . This formula can be used to evaluate binomial expressions raised to noninteger exponents. For Exercises 65-66, use the first four terms of this infinite series to approximate the given expression. Round to 3 decimal places if necessary. 1.334A pizza can be made from either thick or thin crust, and a choice of 6 toppings. How many different types of pizza can be made?A code for an alarm system is made up of two letters, followed by four digits. How many codes can be made if a. There are no restrictions on the letters or digits? b. No letter or digit may be used more than once?A quiz has four true/false questions and six multiple-choice questions. The multiple-choice questions each have five possible answers of which only one is correct. In how many ways can the questions on the test be answered?a. In how many ways can 7 different books be arranged on a bookshelf? b. Determine the number of ways that the letters in the word RIFFRAFF can be arranged.Determine the number of ways that 2 students from a group of 4 students can be selected to hold the positions of president and vice president of student government.A judge at the County Fair must give blue, red, and white ribbons for first-, second-, and third-place entries in a poetry contest. If there are 12 contestants, in how many ways can the judge award the ribbons?Suppose that 20 people enter a raffle. a. In how many ways can four different people among the 20 be selected to receive prizes of 50 each? b. In how many ways can four different people among the 20 be selected to receive prizes of 50,25,10 , and 5 ?The California lottery game “Fantasy 5 � offers a grand prize to a player who selects the correct group of 5 numbers (in any order) from the numbers 1 to 39 . How many groups of 5 numbers are possible?The coach of a co-ed softball team must select 4 women and 5 men from a group of 7 women and 10 men to play in a game. In how many ways can such a team be formed?The fundamental of indicates that if one event can occur in m different ways, and a second event can occur in n different ways, then the two events can occur in sequence in different ways.If n items are arranged in order, then each arrangement is called a of n items.The number of ways that n distinguishable items can be arranged in various orders is .Consider a set of n elements of which one element is repeated r times. Then the number of permutations of the elements of the set is given by .Suppose that n represents the number of distinct elements in a group from which r elements will be chosen in a particular order. Then each arrangement is called a of n items taken at a time.Suppose that n represents the number of elements in a group from which r elements will be selected in no particular order. Then each group selected is called a of n elements taken at a time.The number of permutations of n elements taken r at a time is denoted by nPr and is computed by nPr= or nPr=nn1n2nr+1 .The number of combinations of n elements taken r at a time is denoted by nCr and is computed by .For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain an even number?For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain an odd number?For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain a prime number?For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain a number that is a multiple of 5 ?For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain a number that is a multiple of 10 ?For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is selected, in how many ways can we obtain a number that is divisible by 4 ?15PEDebbie travels several times a year for her job. She takes 4 pairs of slacks, 6 blouses, and 4 scarves, all of different colors. Assuming that the items all match together well, how many different outfits does Debbie have if she selects one item from each category?A license plate has 3 letters followed by 3 digits. a. How many license plates can be made if there are no restrictions on the letters or digits? (See Example 2) b. How many license plates can be made if no digit or letter may be repeated?A security company requires its employees to have a 7 -character computer password that must consist of 5 letters and 2 digits. a. How many passwords can be made if there are no restrictions on the letters or digits? b. How many passwords can be made if no digit or letter may be repeated?The call letters for a radio station must begin with either K or W . a. How many 4 -letter arrangements are possible assuming that letters may be repeated? b. How many 4 -letter arrangements are possible assuming that the letters may not be repeated?An employee identification code for a hospital consists of 2 letters from the set A,B,C,D followed by 4 digits. a. How many identification codes are possible if both letters and digits may be repeated? b. How many identification codes are possible if letters and digits may not be repeated?An online survey is used to monitor customer service. The survey consists of 14 questions. Ten questions have 5 possible responses (strongly agree, agree, neutral, disagree, and strongly disagree). The remaining 4 questions are yes/no questions. In how many different ways can the survey be filled in? (See Example 3)A test consists of 3 multiple-choice questions, each with four possible responses, and 7 true/false questions. In how many ways can a student answer the questions on the test?On a computer, 1 bit is a single binary digit and has two possible outcomes: either 1 or 0 . One byte is 8 bits. That is, a byte is a sequence of 8 binary digits. How many arrangements of 1s and 0s can be made with one byte?Older models of garage door remote controls have a sequence of 10 switches that are individually placed in an up or down position. The remote control can “talk to� the overhead door unit if the 10 corresponding switches in the unit are in the same up/down sequence. How many up/down sequences are possible in an arrangement of 10 switches?a. In how many ways can the letters in the word FLORIDA be arranged? (See Example 4) b. In how many ways can the letters in the word MISSISSIPPI be arranged?a. In how many ways can the letters in the word XRAY be arranged? b. In how many ways can the letters in the word MAMMOGRAM be arranged?In how many ways can the word WRONG be misspelled?In how many ways can the word EXACTLY be misspelled?A delivery truck must make 4 stops at locations A,B,C , and D . Over several weeks, management asks the driver to drive each possible route and record the time required to complete the route. This is to determine the most time-efficient route. How many possible routes are there?In how many ways can 6 people in a family be lined up for a photograph?For Exercises 31-36, evaluate nPr . 6P4For Exercises 31-36, evaluate nPr . 8P5For Exercises 31-36, evaluate nPr . 12P2For Exercises 31-36, evaluate nPr . 11P3For Exercises 31-36, evaluate nPr . 9P9For Exercises 31-36, evaluate nPr . 5P5Evaluate 20P3 and interpret its meaning.Evaluate 15P6 and interpret its meaning.39PEFor Exercises 39-44, evaluate nCr . 8C5For Exercises 39-44, evaluate nCr . 12C242PE43PEFor Exercises 39-44, evaluate nCr . 5C5Evaluate 20C3 and interpret its meaning.Evaluate 15C6 and interpret its meaning.Given A,B,C , a. List all the permutations of two elements from the set. (See Example 5) b. List all the combinations of two elements from the set.Given W,X,Y,Z , a. List all the permutations of three elements from the set. b. List all the combinations of three elements from the set.Suppose that 9 horses run a race. How many first-, second-, and third-place finishes are possible? (See Example 6)In how many ways can a judge award blue, red, and yellow ribbons to 3 films at a film festival if there are 10 films entered?a. In a drama class, 5 students are to be selected from 24 students to perform a synchronized dance, in how many ways can 5 students be selected from the 24 ? (See Example 7) b. Determine the number of ways that 5 students can be selected from the class of 24 to play 5 different roles in a short play.a. There are 100 members of the U.S. Senate. Suppose that 4 senators currently serve on a committee, in how many ways can 4 more senators be selected to serve on the committee? b. In how many ways can a group of 3 U.S. senators be selected from a group of 7 senators to fill the positions of chair, vice-chair, and secretary for the Ethics Committee?A chess tournament has 16 players. Every player plays every other player exactly once. How many chess matches will be played?Suppose that a tennis tournament has 64 players. In how many ways can a pairing for a first-round match be made between 2 players among the 64 players? Assume that each player can play any other player without regard to seeding.In the Minnesota Lotto game “Gopher 5 � a player wins the grand prize by choosing the same group of 5 numbers from 1 through 47 as is chosen by the computer. How many 5 -number groups are possible? (See Example 8)In the New York state lottery game “Lotto� a player wins the grand prize by choosing the same group of 6 numbers from 1 through 59 as is chosen by the computer. How many 6 -number groups are possible?At a ballroom dance lesson, the instructor chooses 3 men and 3 women to demonstrate a new pattern. If there are 9 women and 7 men in the class, in how many ways can the instructor choose 3 men and 3 women? (See Example 9)A committee of 4 men and 4 women is to be made from a group of 12 men and 9 women. In how many ways can such a committee be formed?In a “Pick-4 � game, a player wins a prize for matching a 4-digit number from 0000 to 9999 with the number randomly selected during the drawing. How many 4-digit numbers can a player choose? Assume that a number can start with a zero or zeros such as 0001 .In a “Numbers� game, a player wins a prize for matching a 3-digit number from 000 to 999 with the number randomly selected during the drawing. How many 3-digit numbers can a player choose? Assume that a number can start with a zero or zeros such as 001 .Liza is a basketball coach and must select 5 players out of 12 players to start a game. In how many ways can she select the 5 players if each player is equally qualified to play each position?Jean has a list of 8 books that she knows she must read for a class in the upcoming fall semester of school. She wants to get a head start by reading several of the books during the summer. If she has time in the summer to read 5 of the 8 books, in how many ways can she select 5 books from 8 books?In how many ways can a manager assign 5 employees at a coffee shop to 5 different tasks? Assume that each employee is assigned to exactly one task.In how many ways can a class of 12 kindergarten children line up at the cafeteria?Twenty batteries have been sitting in a drawer for 2yr . There are 4 dead batteries among the 20 . If three batteries are selected at random, determine the number of ways in which a. 3 dead batteries can be selected. b. 3 good batteries can be selected. c. 2 good batteries and 1 dead battery can be selected.There are 30 seeds in a package. Five seeds are defective (will not germinate). If four seeds are selected at random, determine the number of ways in which a. 4 defective seeds can be selected. b. 4 good seeds can be selected. c. 2 good seeds and 2 defective seeds can be selected.A “combination� lock is opened by correctly “dialing� 3 numbers from 0 to 39 , inclusive. The user who knows the code turns the dial to the right to the first number in the code, then to the left to find the second number in the code, and then back to the right for the third number in the code. If someone does not know the code and tries to guess, how many guesses are possible?A palindrome is an arrangement of letters that reads the same way forward and backward. For example, one five-letter palindrome is: ABCBA . a. How many 5 -letter palindromes are possible from a 26 -letter alphabet? b. How many 4 -letter palindromes are possible from a 26 -letter alphabet?A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercises 69-72, determine the number of diagonals for the given polygon. Quadrilateral (4 sides)A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercises 69-72, determine the number of diagonals for the given polygon. Pentagon (5 sides)A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercises 69-72, determine the number of diagonals for the given polygon. Hexagon (6 sides)A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the polygon. For Exercises 69-72, determine the number of diagonals for the given polygon. Octagon (8 sides)For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? The code has no restrictions.For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? The code may not contain repeated digits.For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? The code must represent a 3-digit number.For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? The code must represent a 3-digit number that is a multiple of 5 .For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? The code must represent an even 3-digit number.For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed with the given restrictions? All three digits in the code must be the same.In Exercise 103 from Section 11.3 , we learned that if a fair coin is flipped n times, the number of head/tail arrangements follows a geometric sequence. a. Determine the number of head/tail arrangements if a fair coin is flipped 3 times, 4 times, and 5 times. b. If a couple has 3 children, how many boy/girl sequences are possible for the three births? List the outcomes using “B � for boy and “G � for girl. c. If a couple has 4 children, how many boy/girl sequences are possible for the four births?Social Security numbers assigned in the United States are comprised of 9 digits of the form -- . Would there be enough Social Security numbers for the population of China if the Chinese used the same system? (Hint The population of China is approximately 1.5 billion.)Airlines often oversell seats on an airplane. This is done so that the seats for the few passengers that are no-shows will still have been sold. Sometimes, however, all passengers show up and there are more ticketed passengers than seats. Suppose that one flight has 160 passengers and only 156 seats. Determine the number of ways that the airline can select 4 people at random to place on a different flight.In how many ways can a platoon leader select 4 soldiers among 15 soldiers to secure a building?A car can comfortably hold a family of five. If two people among the five can drive, how many different seating arrangements are possible?A television station must play twelve 30-sec commercials during a half-hour show. In how many ways can the commercials be aired?Consider a horse race with 8 horses. Explain how the fundamental principle of counting or the permutation rule can be used to determine the number of first-, second-, and third-place arrangements.Explain why the number of combinations of n items taken r at a time can be computed by nPrr! .Three biology books, 4 math books, and 2 physics books are to be placed on a bookshelf where the books in each discipline are grouped together. In how many ways can the books be arranged on the bookshelf?A softball team has 9 players consisting of 3 women and 6 men. In how many ways can the coach arrange the batting order if the men must bat consecutively and the women must bat consecutively?A sock drawer has 6 blue socks, 2 white socks, and 12 black socks. If one sock is selected at random, find the probability of the event. a. E1: A blue sock is selected. b. E2: A black sock is selected. c. E3: A brown sock is selected.On a given spin of an American roulette wheel, find the probability of the event. a. E1: The ball lands on the number 7 . b. E2: The ball lands on a red slot. c. E3: The ball does not land on a red slot.Suppose that two dice are rolled. Determine the probability that a. The sum of the numbers showing on the dice is 8 . b. The sum of the numbers showing on the dice is not 8 .Suppose that a committee of three people is to be formed from a group of 8 men and 6 women. Find the probability that the committee will consist of all men.Suppose that of approximately 4,224,100 individuals of age 40 in the United States, 8038 die before the age of 41 and 4,216,062 survive. Determine the probability that a 40-yr -old will live to age 41 .Suppose that one card is drawn at random from a standard deck. Find the probability that a. The card is a 2 or a 10 . b. The card is a 2 or a red card.Refer to the data given in Example 7 . If one student is selected at random from the group, find the probability that a. The student answered “Yes� or “No.� b. The student is male or had no opinion.Suppose that a family plans to have five children. Find the probability that all five children will be girls.Suppose the probability that a person will catch a winter “cold� is 0.16 . What is the probability that four unrelated people will all catch winter “colds�?The of an experiment is the set of all possible outcomes.An is a subset of the sample space of an experiment.If PE=0 , then E is called an event. If PE=1 , then E is called a event.The notation E represents the of event E . Furthermore, PE+PE= .Two events in a sample space are if they do not share any common elements. That is, the two events do not overlap.If two events A and B are not mutually exclusive, then PAB can be computed by the formula PAB= .If two events A and B are mutually exclusive, then PAB= . As a result PAB can be computed from the formula PAB= .For two independent events A and B,PAandB= .Which of the values can represent the probability of an event? a. 1.84 b. 37 c. 0.00 d. 1.00 e. 250 f. 6.1 g. 0.61 h. 6.1Which of the values can represent the probability of an event? a. 2.32 b. 0.231 c. 2.31 d. 1 e. 38 f. 14 g. 2 h. 125For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=0.994For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=1For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=0.75For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=0.003For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=0.05For Exercises 11-16, match the probability with a statement a,b,c,d,e , or f . a. Event E is certain to happen. b. Event E cannot happen. c. Event E is very likely to happen. d. Event E is very unlikely to happen. e. Event E is somewhat likely to happen. f. Event E is as likely to happen as not to happen. PE=0For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number less than 5 is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number less than 3 is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number between 4 and 10 , inclusive, is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number between 2 and 7 , inclusive, is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number greater than 10 , is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number less than 1 , is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number greater than or equal to 1 , is rolled.For Exercises 17-24, consider an experiment where a single 10 -sided die is rolled with the outcomes 1,2,3,4,5,6,7,8,9,10 . Determine the probability of each event. A number less than or equal to 10 , is rolled.A course in early civilization has 6 freshmen, 8 sophomores, and 16 juniors. If one student is selected at random, find the probability of the following events. (See Example1) a. A junior is selected. b. A freshman is selected, c. A senior is selected.Suppose that a box contains 4 chocolate chip cookies, 8 molasses cookies, and 12 raisin cookies, if one cookie is selected at random, find the probability of the following events. a. A chocolate chip cookie is selected. b. A molasses cookie is selected. c. A ginger cookie is selected.For Exercises 27-28, consider an American roulette wheel. (See Example 2) For a given spin of the wheel, find the probability of the following events. a. The ball lands on an even number (do not include 0 and 00 ). b. The ball lands on a number that is a multiple of 5 (do not include 0 and 00 ). c. The ball does not land on the number 8 .For Exercises 27-28, consider an American roulette wheel. (See Example 2) For a given spin of the wheel, find the probability of the following events. a. The ball lands on a black slot. b. The ball lands on a number that is a multiple of 6 (do not include 0 and 00 ). c. The ball does not land on the number 12 .If PE=0.842 , what is the value of PE ?If PE=0.431 , what is the value of PA ?According to the Centers for Disease Control, the probability that a live birth will be of twins in the United States is 0.016 . What is the probability that a live birth will not be of twins?A baseball player with a batting average of 0.291 has a probability of 0.291 of getting a hit for a given time at bat. What is the probability that the player will not get a hit for a given time at bat?For Exercises 33-36, consider the sample space when two fair dice are rolled. (See Example 3) Determine the probabilities for the following events. a. The sum of the numbers on the dice is 4 . b. The sum of the numbers on the dice is not 4 .For Exercises 33-36, consider the sample space when two fair dice are rolled. (See Example 3) Determine the probabilities for the following events. a. The sum of the numbers on the dice is 12 . b. The sum of the numbers on the dice is not 12 .For Exercises 33-36, consider the sample space when two fair dice are rolled. (See Example 3) Determine the probabilities for the following events. a. The sum of the numbers on the dice is greater than 9 . b. The sum of the numbers on the dice is less than 4 .For Exercises 33-36, consider the sample space when two fair dice are rolled. (See Example 3) Determine the probabilities for the following events. a. The sum of the numbers on the dice is greater than or equal to 8 . b. The sum of the numbers on the dice is less than or equal to 5 .After a nationally televised trial, a poll of viewers indicated that 68 thought the defendant was guilty, 22 thought the defendant was not guilty, and the rest were undecided. What is the probability that a person selected from the viewing audience was undecided?If a couple plans to have three children, the probability that all three will be boys is 0.125 . What is the probability that the couple will have at least one girl?Suppose that a jury pool consists of 18 women and 16 men. a. What is the probability that a jury of 9 people taken at random from the pool will consist only of women? (See Example 4) b. What is the probability that the jury will consist only of men? c. Why do the probabilities from parts (a) and (b) not add up to 1 ?Suppose that 20 good batteries and 6 defective batteries are in a drawer. a. If 4 batteries are drawn at random, what is the probability that all four will be defective? b. What is the probability that all four will be good? c. Why do the probabilities from parts (a) and (b) not add up to 1 ?In the Illinois state lottery game “Little Lotto,� a player wins the grand prize by choosing the same group of five numbers from 1 through 39 as is chosen by the computer. What is the probability that a player will win the grand prize by playing 1 ticket?In the New York state lottery game “Lotto,� a player wins the grand prize by choosing the same group of 6 numbers from 1 through 59 as is chosen by the computer. What is the probability that a player will win the grand prize by playing 5 different tickets?Scientist Gregor Mendel (1822-1884) is often called the “father of modem genetics� and is famous for his work involving the inheritance of certain traits in pea plants. Suppose that the genes controlling the color of peas are Y for yellow and y for green. Each plant has two genes, one from the female (seed) and one from the male (pollen). The Y gene is dominant, and therefore a plant with genes YY will have yellow peas, a plant with genes Yy or yY will have yellow peas, and a plant with genes yy will have green peas. If a plant with two yellow genes YY is crossed with a plant with two green genes yy , the result is four hybrid offspring with genotypes Yy . The offspring will be yellow, but will carry the recessive green gene. Suppose that both parent pea plants are hybrids with genotype Yy . a. Make a chart showing the possible genotypes of the offspring. b. What is the probability that a given offspring will have green peas? c. What is the probability that a given offspring will have yellow peas?Scientist Gregor Mendel (1822-1884) is often called the “father of modem genetics� and is famous for his work involving the inheritance of certain traits in pea plants. Suppose that the genes controlling the color of peas are Y for yellow and y for green. Each plant has two genes, one from the female (seed) and one from the male (pollen). The Y gene is dominant, and therefore a plant with genes YY will have yellow peas, a plant with genes Yy or yY will have yellow peas, and a plant with genes yy will have green peas. If a plant with two yellow genes YY is crossed with a plant with two green genes yy , the result is four hybrid offspring with genotypes Yy . The offspring will be yellow, but will carry the recessive green gene. Suppose that one parent pea plant has genotype YY and the other has genotype Yy . a. Make a chart showing the possible genotypes of the offspring. b. What is the probability that a given offspring will have green peas? c. What is the probability that a given offspring will have yellow peas?At a hospital specializing in treating heart disease, it was found that 222 out of 4624 patients undergoing open heart mitral valve surgery died during surgery or within 30 days after surgery. Determine the probability that a patient will not survive the surgery or 30 days after the surgery. This is called the mortality rate. Round to 3 decimal places. (See Example 5)China has the largest population of any country with approximately 1.5 billion people. In a recent year, census results indicated that 199,500,000 Chinese were over the age of 60 .If a person is selected at random from the population of China, what is the probability that the person is over 60 years old? Round to 3 decimal places.For a certain district, a random sample of registered voters results in the distribution by political party given in the graph. Based on these results, what is the probability of selecting a voter at random from the district and getting a. A Democrat? b. A voter who is neither Democrat Republican, nor independent?The final exam grades for a sample of students in a Freshmen English class at a large university result in the following grade distribution. Based on these results, what is the probability of selecting a student at random taking Freshmen English and getting a student who received a. AnA. b. AC.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A jack or a queen.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is An ace or a 2 .For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A jack or a diamond.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A 5 or a heart.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A face card (jack, queen, or king)For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A card numbered between 5 and 10 , inclusive.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A face card or a red card.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A card numbered between 5 and 10 , inclusive, or a block card.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is A heart, club, or spade.For Exercises 49-58, consider the sample space for a single card drawn from a standard deck. (See Example 6 and Figure 11-12) Find the probability that the card drawn is An ace, 2 , or 3 .For Exercises 59-66, use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. (See Example 7) The person has elevated cholesterol.For Exercises 59-66, use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. (See Example 7) The person is 61 or older.For Exercises 59-66, use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. (See Example 7) The person is 60 or under.For Exercises 59-66, use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. (See Example 7) The person is 31 or olderFor Exercises 59-66, use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. (See Example 7) The person has normal cholesterol or is 61 or older.64PE65PE66PE67PEIf a code for an alarm is a 4-digit sequence, determine the probability that someone guesses each digit correctly.69PE70PEIn the 2010 Wimbledon Championships, John Isner from the United States and Nicolas Mahut from France played a first-round tennis match that became the longest match in tennis history. (The match stretched over a 3-day period with Isner winning 70-68 in the fifth set.) In 2011 , after a random draw, the two men met again in the first round of Wimbledon. This is highly improbable. If there are 128 men in the tournament, estimate the probability that a. Isner and Mahut would meet in the first round at Wimbledon in any given year. Assume that any player can play any other player in the first round (that is, disregard the fact that seeded players do not play one another in the first round). b. Isner and Mahut would meet in the first round 2yr in a row.72PE73PEA quiz has 6 multiple-choice questions and each question has 5 possible responses of which exactly one is correct Find the probability that a student answers each question incorrectly.The blood type of an individual is classified according to the presence of certain antigens, substances that cause the immune system to produce antibodies. These antigens are denoted by A,B , and Rh . If an individual's blood contains either the A or B antigen, these letters are listed in the blood type. If neither A nor B is present, then the letter O is used. If the Rh antigen is present, the blood is said to be Rh positive Rh+ ; otherwise, the blood is Rh negative Rh . Under this system, a person with AB+ blood has all three antigens, and group O is absent all three antigens. The distribution of blood types for people living in the United States is given in the table. Refer to the table for Exercises 75-78. Round to 3 decimal places when necessary. a. If an individual is randomly selected from the population, find the probability that the individual will have the Rh factor, b. If three people are selected at random, find the probability that they all have the Rh factor.76PE77PE78PE79PE80PE81PE82PEA slot machine in a casino has three wheels that all spin independently. Each wheel has 11 stops, denoted by 0 through 9 , and bar. What is the probability that a given outcome is bar-bar-bar?84PE85PEFor Exercises 86-88, a. Shade the area bounded by the given inequalities on a coordinate grid showing 5x5 and 5y5 . b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by 5x5 and 5y5 . Find the probability that a dart thrown at the target will land in the shaded region. yxandy487PE88PE89PE90PE91PE92PESuppose that a box of DVDs contains 10 action movies and 5 comedies. a. If two DVDs are selected from the box with replacement, determine the probability that both are comedies. b. It probably seems more reasonable that someone would select two different DVDs from the box. That is, the first DVD would not be replaced before the second DVD is selected. In such a case, are the events of selecting comedies on the first and second picks independent events? c. If two DVDs are selected from the box without replacement, determine the probability that both are comedies.94PE95PE96PE