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mathematics
calculus

Questions and Answers of Calculus

A card is drawn at random from a deck of 52 playing cards. Find the probability that it is a club or a king.
A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 560 who favored raising the age, 390 were female. Of the 440 opposition responses, 160 were female. A
The probability that a wife watches a certain television show is 0.55, that her husband watches it is 0.45, and that both watch the show is 0.30. What is the probability that the husband or the wife
If a ball is drawn, what is the probability that (a) The ball is red and even-numbered? (b) The ball is red or even-numbered? A bag contains 5 red balls numbered 1, 2, 3, 4, 5 and 9 white balls
If a ball is drawn, what is the probability that it is (a) White and odd-numbered? (b) White or odd-numbered? (c) White or even-numbered? A bag contains 5 red balls numbered 1, 2, 3, 4, 5 and 9 white
A card is drawn from a deck of 52 playing cards. Given that it is a red card, what is the probability that (a) It is a heart? (b) It is a king?
A die is rolled and a coin is tossed. What is the probability that the die shows an even number and the coin toss results in a head?
(a) A coin is tossed three times. What is the probability of getting a head on all three tosses?(b) A coin is tossed three times. What is the probability of getting at least one tail?
The probability that Sam will win in a certain game whenever he plays is 2/5. If he plays two games, what is the probability that he will win just the first game?
(a) A box contains 3 red balls, 2 white balls, and 5 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of
(a) One card is drawn at random from a deck of 52 cards. The first card is replaced, and a second card is drawn. Find the probability that both are hearts.(b) Answer the question in part (a) if the
Two balls are drawn from a bag containing 3 white balls and 2 red balls. If the first ball is replaced before the second is drawn, what is the probability that (a) Both balls are red? (b) Both balls
If the first ball is not replaced before the second is drawn. Two balls are drawn from a bag containing 3 white balls and 2 red balls. If the first ball is replaced before the second is drawn, what
A bag contains 9 nickels, 4 dimes, and 5 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel, a quarter, and a nickel, in
A card is drawn from a deck of 52 playing cards. Given that it is an ace, king, queen, or jack, what is the probability that it is a jack?
A bag contains 6 red balls and 8 green balls. If two balls are drawn together, find the probability that (a) Both are red. (b) Both are green.
A red ball and 4 white balls are in a box. If two balls are drawn, without replacement, what is the probability (a) Of getting a red ball on the first draw and a white ball on the second? (b) Of
From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that (a) The first will be a king and the second will be a jack? (b) The first
One card is drawn at random from a deck of 52 cards. The first card is not replaced, and a second card is drawn. Find the probability that (a) Both cards are spades. (b) The first card is a heart and
Two cards are drawn from a deck of 52 cards. What is the probability that both are aces (a) If the first card is replaced before the second is drawn? (b) If the cards are drawn without replacement?
Two balls are drawn, without replacement, from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that (a) The second ball is red, given that the
A red die and a green die are rolled. What is the probability that a 6 results on the green die and that a 4 results on the red die?
What is the probability that a person selected at random from this group will favor reducing industries' carbon emissions, given that the person is a Democrat?The table gives the results of a survey
What is the probability that a person selected at random from this group will oppose reducing industries' carbon emissions, if the person is a Republican?The table gives the results of a survey of
If the group surveyed represents the people of the United States, what is the probability that a citizen selected at random will favor reducing industries' carbon emissions, given that the person is
A die has been "loaded" so that the probability of rolling any even number is 2/9 and the probability of rolling any odd number is 1/9. What is the probability of (a) Rolling a 6, given that an even
If the group surveyed represents the people of the United States, what is the probability that a citizen selected at random will oppose reducing industries' carbon emissions, given that the person is
Given that a randomly selected individual is non-White, find the probability that he or she opposes oil drilling in national parks.Suppose the table summarizes the opinions of various groups on the
Given that a randomly selected individual is a Democrat, find the probability that he or she opposes oil drilling in national parks.Suppose the table summarizes the opinions of various groups on the
Given that a randomly selected individual is in favor of oil drilling in national parks, find the probability that he or she is a Republican.Suppose the table summarizes the opinions of various
Given that a randomly selected individual is opposed to oil drilling in national parks, find the probability that he or she is a Democrat.Suppose the table summarizes the opinions of various groups
Find the probability that a person who favors oil drilling in national parks is non-WhiteSuppose the table summarizes the opinions of various groups on the issue of oil drilling in national parks.
A die has been "loaded" so that the probability of rolling any even number is 2/9 and the probability of rolling any odd number is 1/9. What is the probability of (a) Rolling a 5? (b) Rolling a 5,
A name is drawn at random from the 96 entrants in a golf tournament. The person whose name is selected draws a ball from a bag containing four balls, one of which is embossed with the Peggos Company
Each computer component that the Peggos Company produces is tested twice before it is shipped. There is a 0.7 probability that a defective component will be so identified by the first test and a 0.8
Suppose a birth control pill is 99% effective in preventing pregnancy. (a) What is the probability that none of 100 women using the pill will become pregnant? (b) What is the probability that at
If a fighter pilot has a 4% chance of being shot down on each mission during a war, what is the probability that he will not be shot down in 25 missions?
Twenty-three percent of the cars owned by a car rental firm have some defect. What is the probability that of 3 cars selected at random, (a) None has a defect? (b) At least one has a defect?
An unprepared student must take a 7- question multiple-choice test that has 5 possible answers per question. If the student guesses on every question, what is the probability that (a) She will answer
An unprepared student must take a 7- question multiple-choice test that has 5 possible answers per question. If the student can eliminate two of the possible answers on the first three questions, and
What is the probability that a student who guesses on every question of a 10-question true-or-false test will get at least one answer correct?
Suppose that the odds in favor of the horse Portia winning a race are 3:8 and that the odds of the horse Trinka winning the same race are 1:10. What is the probability that Portia or Trinka will win
Suppose that the odds that Blackjack will win a race are 1 to 3 and the odds that Snowball will win the same race are 1 to 5. If only one horse can win, what odds should be given that one of these
Assuming there are 365 different birthdays, find the probability that two people chosen at random will have (a) Different birthdays. (b) The same birthday.
Assuming there are 365 different birthdays, find the probability that of three people chosen at random,(a) No two will have the same birthday.(b) At least two will have the same birthday.
Assuming there are 365 different birthdays, find the probability that of 20 people chosen randomly, (a) No two will have the same birthday. (b) At least two will have the same birthday.
A bag contains 4 red balls and 6 white balls. Two balls are drawn without replacement. (a) What is the probability that the second ball is white, given that the first ball is red? (b) What is the
A fair coin is tossed 3 times. Find the probability of (a) Throwing 3 heads, given that the first toss is a head. (b) Throwing 3 heads, given that the first two tosses result in heads.
A bag contains 5 coins, 4 of which are fair and 1 that has a head on each side. If a coin is selected from the bag and tossed twice, what is the probability of obtaining 2 heads? Use probability
A bag contains 13 blue balls and 7 red balls. If 2 balls are drawn at random from the bag, with the first ball being replaced before the second ball is drawn, what is the probability that (a) The
A bag contains 4 white balls and 6 red balls. What is the probability that if 2 balls are drawn (with replacement), (a) The first ball is red and the second is white? (b) Both balls are red? (c) One
Two balls are drawn, without replacement, from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that (a) The second ball is even-numbered, given
An urn is selected at random and a ball is drawn. If the ball is green, find the probability that urn III was selected. Use (a) a probability tree and (b) Bayes' formula to find the probabilities.
An urn is selected at random and a ball is drawn. If the ball is red, what is the probability that urn III was selected? Use (a) a probability tree and (b) Bayes' formula to find the probabilities.
There are 3 urns containing coins. Urn I contains 3 gold coins, urn II contains 1 gold coin and 1 silver coin, and urn III contains 2 silver coins. An urn is selected and a coin is drawn from the
In Problem 15, what is the probability that the urn selected was urn III if the coin selected was silver? Use (a) a probability tree and (b) Bayes' formula to find the probabilities.
Lactose intolerance affects about 20% of non-Hispanic White Americans, 50% of Hispanic Americans, and 75% of African, Asian, and Native Americans. Seventy-six percent of U.S. residents are
What is the probability that a couple will have at least two sons if they plan to have 3 children and if the probability of having a son equals the probability of having a daughter?
Suppose that a marksman hits the bull's-eye 15,000 times in 50,000 shots. If the next 4 shots are independent, find the probability that(a) The next 4 shots hit the bull's-eye.(b) Two of the next 4
A bag contains 4 balls: 2 red, 1 white, and 1 green. Two balls are drawn without replacement. Find the probability that 2 different colors are drawn, given that(a) The first ball is not white.(b) The
In a random survey of students concerning student activities, 30 engineering majors, 25 business majors, 20 science majors, and 15 liberal arts majors were selected. If two students are selected at
Suppose a box contains 3 defective transistors and 12 good transistors. If 2 transistors are drawn from the box without replacement, what is the probability that (a) The first transistor is good and
The probability that an individual without a college education earns more than $50,000 is 0.2, whereas the probability that a person with a B.S. or higher degree earns more than $50,000 is 0.6. The
A small town has 8000 adult males and 6000 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from
One hundred boys and 100 girls were asked if they had ever been frightened by a television program. Thirty of the boys and 60 of the girls said they had been frightened. One of these children is
A candidate for public office knows that he has a 60% chance of being elected to the office if he is nominated by his political party and that his party has a 50% chance of winning with another
A self-administered pregnancy test detects 85% of those who are pregnant but does not detect pregnancy in 15%. It is 90% accurate in indicating women who are not pregnant but indicates 10% of this
A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 560 who favored raising the age, 390 were female. Of the 440 who expressed opposition, 160 were
In a Student Activity Participation Study (SAPS) survey, 30 engineering majors, 25 business majors, 20 science majors, 15 liberal arts majors, and 10 human development majors were selected. Ten of
An urn contains 4 red, 5 white, and 6 black balls. One ball is drawn from the urn, it is not replaced, and a second ball is drawn. (a) What is the probability that both balls are white? (b) What is
If a student is selected at random from the group in Problem 29, what is the probability the student is (a) An engineering major, given that she is female? (b) An engineering major, given that he is
An urn contains 4 red, 5 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn.(a) What is the probability that both balls are white?(b) What is the
Three balls are drawn, without replacement, from a bag containing 4 red balls and 5 white balls. Find the probability that(a) Three white balls are drawn.(b) Two white balls and one red ball are
An urn contains 4 red, 5 white, and 6 black balls. Three balls are drawn, without replacement, from the urn.(a) What is the probability that all three balls are red?(b) What is the probability that
A bag contains 4 white balls and 6 red balls. Three balls are drawn, without replacement, from the bag.(a) What is the probability that all three balls are white?(b) What is the probability that
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 heads will
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 heads will
If (n + 1)! = 17n!, find n.
If (n + 1)! = 30(n - 1)!, find n.
Mercedes Benz E-Class sedans are converted to limousines by a coach company. The limousines, named Binz, come in two models, XL Six Door and XL Vis-à-Vis, and are available with a choice of 2
Baskin Robbins' logo includes "31" because its stores offer 31 flavors of ice cream cones in sizes small, medium, and large. (a) How many different selections of cones are possible if each cone has
1. If a state wants each of its license plates to contain 7 different digits, how many different license plates can it make? 2. If a state wants each of its license plates to contain any 7 digits,
1. Four candidates for manager of a department store are ranked according to the weighted average of several criteria. How many different rankings are possible if no two candidates receive the same
1. A department store manager wants to display 6 brands of a product along one shelf of an aisle. In how many ways can he arrange the brands? 2. The call letters for radio stations begin with K or W,
1. How many ways can a 10-question multiple-choice test be answered if each question has 4 possible answers? 2. A flush (5 cards from the same suit) is an excellent hand in poker. If there are 13
South Carolina previously had license plates containing two letters followed by four digits but now has plates with three letters followed by three digits. How many more plates are now available?
1. If 8 people are qualified for the next flight of a new space vehicle, how many different groups of 3 people can be chosen for the flight? 2. A traveling salesperson has 30 products to sell but has
1. A psychological study of outstanding salespeople is to be made. If 5 salespeople are needed and 12 are qualified, in how many ways can the 5 be selected? 2. A company wishes to use the services of
A sociologist wants to pick 3 fifth-grade students from each of four schools. If each of the schools has 50 fifth-grade students, how many different groups of 12 students can he select? (Set up in
In how many ways can a committee consisting of 6 men and 6 women be selected from a group consisting of 20 men and 22 women?
In how many ways can a hand consisting of 6 spades, 4 hearts, 2 clubs, and 1 diamond be selected from a deck of 52 cards?
1. The Iranian government issued an order requiring minibuses in Tehran to have separate sections to avoid millions of "sins," because every day 370,000 women ride the minibuses (Source: USA Today).
How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9(a) If each digit may be used once in each number?(b) If each digit may be used repeatedly in each number?
If a child is given cards with A, C, D, G, O, and T on them, what is the probability he or she could spell DOG by guessing the correct arrangement of 3 cards from the 6?
If a license plate has seven different digits, what is the probability that it contains a zero?
1. As a reward for a record year, the Ace Software Company is randomly selecting 4 people from its 500 employees for a free trip to Hawaii, but it will not pay for a traveling companion. If John and
In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct?
In a 10-question matching test with 15 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct?
A box of 12 transistors has 3 defective ones. If 2 transistors are drawn from the box together, what is the probability(a) That both transistors are defective?(b) That neither transistor is
Suppose that 6 transistors are drawn at random from a box containing 18 good transistors and 2 defective transistors. What is the probability that (a) All 6 of the transistors are good? (b) Exactly 4

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