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mathematics
mathematical applications for the management
Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions
Because of a firm’s growth, it is necessary to transfer one of its employees to one of its branch stores. Three of the nine employees are women, and all of the nine employees are equally qualified for the transfer. If the person to be transferred is chosen at random, what is the probability that
Fifty-one percent of the U.S. population are female, and 23.6% of the female population have college degrees. If a U.S. resident is chosen at random, what is the probability that the person is a female with a college degree?
Lactose intolerance affects about 75% of African, Asian, and Native Americans. If a person is selected from this group of people, what is the probability that the person will have lactose intolerance?
In the pretrial hearing of the O. J. Simpson case, the prosecution stated that Mr. Simpson’s blood markers included type A blood, which 33.7% of the population has; blood SD subtype 1, which 79.6% of the population has; and PGM 2122, which 1.6% of the population has. If these blood markers are
A company selling substandard drugs to developing countries sold 2,000,000 capsules with 60,000 of them empty. What is the probability that a person who takes a randomly chosen capsule from this company will get an empty capsule?
On July 25, 2016, two amateur golfers, ages 10 and 13, hit back-to-back holes in one at the Country Club of Hilton Head on Hilton Head Island, South Carolina. According to the National Hole-in-One Association, the probability of an amateur golfer getting a hole in one is 1/12,000. If the golfer’s
Among the population of Houston, 41.9% are of Hispanic descent. What is the probability that a Houston resident chosen at random is(a) Of Hispanic descent?(b) Not of Hispanic descent?
Among the residents of Los Angeles, 13% are classified as of Asian descent. If an L.A. resident is chosen at random, what is the probability that he or she is(a) Of Asian descent?(b) Not of Asian descent?
Suppose the table summarizes the opinions of various groups on the issue of oil drilling in national parks. Use this table to calculate the empirical probabilities in Problems.Find the probability that an individual is a White Republican opposed to oil drilling in national parks. Whites Non-Whites
In a manufacturing process where 8% of all items are defective, an inspector at the end of the production line selects some items for inspection. Suppose that 64% of the defective items and 16% of the good items go through the inspection. Find the probability that an item(a) Has an inspection.(b)
Sixteen percent of the population of the United States has a negative Rh (Rhesus) factor in their blood, and the remainder has a positive Rh factor. What is the probability that a resident of the United States chosen at random(a) Will have a negative Rh factor?(b) Will have a positive Rh factor?
Four percent of the population of the United States has type AB blood. What is the probability that a U.S. resident chosen at random(a) Will have type AB blood?(b) Will not have type AB blood?
Sixty men out of 1000 and 3 women out of 1000 are color blind. A person is picked at random from a group containing 10 men and 10 women.(a) What is the probability that the person is color blind?(b) What is the probability that the person is a man if the person is color blind?
In the United States in 2014, there were 614,348 deaths from heart disease, 591,699 from cancer, and 133,103 from stroke. If a death is chosen at random from the 2,596,993 deaths that occurred in 2014, what is the probability that the cause of death was from cancer or stroke?
In a survey of 350 registered voters in Belair, 123 said that they would vote for the Democratic candidate for mayor. If a registered voter is selected at random, what is the probability that this person will vote for the Democratic candidate?
Rob Lee knows that he can compete successfully in a single track mountain bike race unless he gets a flat tire or his chain breaks. In such races, the probability of getting a flat is 0.3, of the chain breaking is 0.06, and of both occurring is 0.01. What is the probability that Rob completes the
Suppose a factory has three machines (I, II, and III) that produce identical items as follows:I: 500 items per day; 1% defectiveII: 200 items per day; 5% defectiveIII: 300 items per day; 3% defectiveSuppose one item is selected at random and tested. Find the probability that item(a) Is
A state wants each of its license plates to contain 7 digits. How many different license plates can it make if(a) All the digits are different?(b) Any 7 digits may be used?
Write the transition matrix for his selection of a car.Use the following information for Problems. A man owns an Audi, a Ford, and a VW. He drives every day and never drives the same car two days in a row. These are the probabilities that he drives each of the other cars the next day:Pr(Ford after
An unprepared student must take a 7-question multiple-choice test that has 5 possible answers per question. If the student guesses on the first question, what is the probability that she will answer that question incorrectly?
Suppose that four of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0?
A restaurant has an early dining fixe Prix (fixed price) dinner special that offers one soup or salad from 5 available, one entrée from 5 chef’s specials, and one dessert from 4 choices.(a) How many different fixes Prix dinners are possible?(b) Suppose one particular diner wants a salad and a
Ideally, auto insurance rates are lower for good drivers than for bad drivers, but an insurer needs to be able to tell which type of driver a client is. Assume that all drivers are considered as either “good drivers” or “bad drivers” and that the probability of a random driver being a
The new Volvo XC90 Twin-Engine Plug-in Hybrid has a self-programmable mode with four different powertrain settings, three settings for the air suspension, three for the steering, three for the instrument display, two for the brakes, and two for the climate control.(a) How many differently set cars
Of 100 students, 24 can speak French, 18 can speak German, and 8 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?
The most common HIV test is the Enzyme Immunoassay (EIA) Test. When a subject’s HIV condition is known, the following probabilities about the EIA test are known.Pr(Test(+) I HIV(+)) = 0.9985Pr(Test(-) I HIV(-)) = 0.994(a) Find Pr(Test(-) I HIV(+)), the probability of a false negative.(b) Find
According to the American Cancer Society, 199 of 200 mammograms turn out to be normal. What is the probability that the mammogram of a woman chosen at random will turn out to be normal?
An unprepared student must take a 7-question multiple-choice test that has 5 possible answers per question. If the student guesses on the first question, what is the probability that she will answer that question incorrectly?
Forty-six percent of marijuana use among youth occurs in the inner cities. If an instance of such marijuana use is chosen at random, what is the probability that the use occurs in an inner-city?
What is the transition matrix for this information?Use the following information for Problems. The probability that daughters of a mother who attends church regularly will also attend church regularly is 0.8, whereas the probability that daughters of a mother who does not attend regularly will
A publishing company has determined that a new edition of an existing mathematics textbook will be readopted by 80% of its current users and will be adopted by 7% of the users of other texts if the text is not changed radically. To determine whether it should change the book radically to attract
If nC8 = nC7, find n.
The probability that an individual without a college education earns more than $100,000 is 0.2, whereas the probability that a person with a B.S. or higher degree earns more than $100,000 is 0.6. The probability that a person chosen at random has a B.S. degree is 0.3. What is the probability that a
Garage door openers have 10 on-off switches on the opener in the garage and on the remote control used to open the door. The door opens when the remote control is pressed and all the switches on both the opener and the remote agree.(a) How many different sequences of the on-off switches are
If nC6 = nC4, find n.
Forty-six percent of marijuana use among youth occurs in the inner cities. If an instance of such marijuana use is chosen at random, what is the probability that the use does not occur in an inner-city?
Compute 7C3.
Suppose a box contains 3 defective batteries and 12 good batteries. If 2 batteries are drawn from the box without replacement, what is the probability that(a) The first one is good and the second one is defective?(b) The first one is defective and the second one is good?(c) One of the batteries
If the probability that an event E will not occur is 8/11, what are the odds(a) That E will occur?(b) That E will not occur?
NACO Body Shops has found that 14% of the cars on the road need to be painted and that 3% need major bodywork and painting. What is the probability that a car selected at random needs major bodywork if it is known that it needs to be painted?
Compute
In Problems, find the steady-state vector associated with the given transition matrix from Problems 9–12. 0.8 0.1 0.1 D = 0.2 0.6 0.2 _ 0.3 0.3 0.4
A ball is drawn from a bag containing 13 red balls numbered 1–13 and 5 white balls numbered 14–18. What is the probability that the ball is(a) Not red?(b) White and odd-numbered?(c) White or odd-numbered?(d) Neither white nor odd-numbered?
Compute 6P2.
If the probability that an event will occur is 2/5, what are the odds(a) In favor of the event occurring?(b) Against the event occurring?
A car rental firm has 350 cars. Seventy of the cars have only defective windshield wipers and 25 have only defective taillights. Two hundred of the cars have no defects; the remainder have other defects. What is the probability that a car chosen at random(a) Has defective windshield wipers?(b) Has
Compute 5.
Lactose intolerance affects about 20% of non-Hispanic White Americans and 50% of White Hispanic Americans. Nine percent of Americans are Hispanic Whites, and 75.6% are non-Hispanic Whites. If a White American is chosen at random and is lactose-intolerant, what is the probability that he or she is
Compute 3C1.
A placement test is given by a university to predict student success in a calculus course. On average, 70% of students who take the test pass it, and 87% of those who pass the test also pass the course, whereas 8% of those who fail the test pass the course.(a) What is the probability that a student
Compute 4C4.
A cube has 2 faces painted red, 2 painted white, and 2 painted blue. What is the probability of getting a red face or a white face in one roll?
Suppose that 6 batteries are drawn at random from a box containing 18 good batteries and 2 defective ones. What is the probability that(a) All 6 are good?(b) Exactly 4 are good?(c) Exactly 2 are good?
Computer chips come from two suppliers, with 80% coming from supplier 1 and 20% coming from supplier 2. Six percent of the chips from supplier 1 are defective, and 8% of the chips from supplier 2 are defective. If a chip is chosen at random, what is the probability that it is defective?
Compute 80C76.
A box of 12 batteries has 3 defective ones. If 2 batteries are drawn from the box together, what is the probability that(a) Both are defective?(b) Neither one is defective?(c) One is defective?
The multistate “5 of 50” game draws 5 balls without replacement from 50 balls numbered 1–50.(a) How many different drawing results are possible if order does not matter?(b) What is the probability that a person holding one ticket will win (match all the numbers drawn)?
Compute 100C98.
A bag contains 8 white balls, 5 red balls, and 7 black balls. If 3 balls are drawn at random from the bag, without replacement, what is the probability that(a) The first two balls are red and the third is black?(b) The third ball is black given that the first is black?
The state of Arizona has a “6 of 42” game in which 6 balls are drawn without replacement from 42 balls numbered 1–42. The order in which the balls are drawn does not matter.(a) How many different drawing results are possible?(b) What is the probability that a person holding one ticket will
A bag contains 8 white balls, 5 red balls, and 7 black balls. If 3 balls are drawn at random from the bag, with replacement, what is the probability that(a) The first two balls are red and the third is black?(b) 2 of the balls are red and 1 is black?
In Problems, use (a) a probability tree and (b) Bayes’ formula to find the probabilities.In Problems, each of urns I and II has 5 red balls, 3 white balls, and 2 green balls. Urn III has 1 red ball, 1 white ball, and 8 green balls.An urn is selected at random, and a ball is drawn. If the ball is
In a group of 20 people, 15 are right-handed, 4 are lefthanded, and 1 is ambidextrous. If 2 people are selected at random, without replacement, use a tree to find the following probabilities.(a) Both are left-handed.(b) One is right-handed, and one is left-handed.(c) Two are right-handed.(d) Two
Suppose a die is biased (unfair) so that each odd-numbered face has probability of 1/4 of resulting and each even face has probability of 1/12 of resulting. Find the probability of getting a number greater than 3.
A box contains 2 red balls and 3 black balls. Two balls are drawn from the box without replacement. Find the probability that(a) The first ball is black and the second is red.(b) The second ball is red, given that the first ball is black.
In Problems, use(a) A probability tree and(b) Bayes’ formula to find the probabilities.In Problems, each of urns I and II has 5 red balls, 3 white balls, and 2 green balls. Urn III has 1 red ball, 1 white ball, and 8 green balls.An urn is selected at random, and a ball is drawn. If the ball is
In a group of 20 people, 15 are right-handed, 4 are lefthanded, and 1 is ambidextrous. What is the probability that a person selected at random is(a) Left-handed?(b) Ambidextrous?
Find (2n + 2)!/(2n)!
In Problems, one ball is drawn from a bag containing 5 red balls numbered 1–5 and 9 white balls numbered 6–14. In each case, find the probability that the ball is(a) Divisible by 3 and by 2.(b) Divisible by 3 or by 2.(c) Not divisible by 15.
A bag contains 4 red balls and 3 black balls. Two balls are drawn at random from the bag without replacement. Find the probability that(a) Both balls are red.(b) One is red and one is black.
In a certain region of the country with a large number of cars, 45% of the cars are from Asian manufacturers, 35% are American, and 20% are European. If 3 cars are chosen at random, what is the probability that 2 American cars are chosen?
A die is thrown twice. What is the probability that a 3 will result the first time and a 6 the second time?
Find (n - 1)!/2n!.
In Problems, one ball is drawn from a bag containing 5 red balls numbered 1–5 and 9 white balls numbered 6–14. In each case, find the probability that the ball is(a) Divisible by 3 and by 7.(b) Divisible by 3 or by 7.(c) Not divisible by 3.
In Problems, use probability trees to find the probabilities of the indicated outcomes.Two chips are drawn without replacement from a bag that contains 9 black chips numbered 1–9 and 4 white chips numbered 10–13. Find the probability that(a) The first chip is odd-numbered given that the second
A cat hits the letters on a computer keyboard three times. What is the probability that the word RAT appears?
A fair coin is tossed 14 times. What is the probability of tossing 14 heads, given that the first 13 tosses are heads?
Compute nP1.
In Problems, one ball is drawn from a bag containing 5 red balls numbered 1–5 and 9 white balls numbered 6–14. In each case, find the probability that the ball is(a) White and odd-numbered.(b) White or odd-numbered.(c) White or even-numbered.
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems.The first ball is black, given that the second ball is white.
Compute nPn.
In Problems, one ball is drawn from a bag containing 5 red balls numbered 1–5 and 9 white balls numbered 6–14. In each case, find the probability that the ball is(a) Red and even-numbered.(b) Red or even-numbered.(c) Not divisible by 3.
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems. The second ball is white. (Use a tree.)
A fair die is rolled. Find the probability that the result is a 4, given that the result is even.
How many four-digit numbers can be formed from the digits 1, 4, 5, 7, 8, and 9(a) If the numbers must be even and digits are not used repeatedly?(b) If the numbers are less than 3000 and digits are not repeated?
If the probability that an event will occur is 7/9, what is the probability that the event will not occur?
In Problems, use probability trees to find the probabilities of the indicated outcomes.A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, what is the probability that(a) Heads will occur
If the probability that event E will occur is 3/5, what is the probability that E will not occur?
(a) In how many different orders can the letters R, A, N, D, O, M be written?(b) If the letters R, A, N, D, O, M are placed in random order, what is the probability that they will spell RANDOM?
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems.(a) The first ball is white, and the second ball is black.(b) A white ball and a black ball are drawn.
If one ball is drawn from the bag in Problem 5, what is the probability that the ball is white, given that the ball is odd-numbered?
Compute 3P3.
A die is rolled. Find the probability of getting a number greater than 0.
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems.Both balls are white.
A bag contains 9 red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 6 white balls numbered 10, 11, 12, 13, 14, 15. One ball is drawn from the bag. What is the probability that the ball is red, given that the ball is even-numbered?
An ordinary die is tossed. What is the probability of getting a number divisible by 3 or an odd number?
An ordinary die is tossed. What is the probability of getting a 3 or a 4?
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems.The sum of the numbers is 7.
In Problems, one card is drawn from a deck of 12 cards numbered 1 through 12. In each case, find the probability that the card is(a) Divisible by 3 and by 5.(b) Divisible by 3 or by 5.
If you draw one card at random from a deck of 12 cards numbered 1 through 12, inclusive, what is the probability that the number you draw is divisible by 4?
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