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nature of mathematics

Questions and Answers of Nature Of Mathematics

Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P\) (four or five) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) even \()\) THE 36 WAYS DICE CAN ROLE O 8
Use the sample space shown in Figure13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice.Figure 13.5\(P(\) eight \(o r\) ten \()\) THE 36 WAYS DICE CAN ROLE
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Suppose you and an opponent each pick one of the spinners shown here. A "win" means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners
Perform the experiments in Problems 48-51, tally your results, and calculate the probabilities (to the nearest hundredth).Toss a coin 100 times. Make sure that, each time the coin is flipped, it
Perform the experiments in Problems 48-51, tally your results, and calculate the probabilities (to the nearest hundredth).Roll a pair of dice 100 times.Keep a record of the results. Based on your
Perform the experiments in Problems 48-51, tally your results, and calculate the probabilities (to the nearest hundredth).Flip three coins simultaneously 100 times, and note the results. The possible
Perform the experiments in Problems 48-51, tally your results, and calculate the probabilities (to the nearest hundredth).Simultaneously toss a coin and roll a die 100 times, and note the outcome of
Suppose it is certain that an earthquake will occur someday. What is the probability (to the nearest percent) that it will occur while you are at work? Assume you are at work 8 hours per day, 240
Suppose it is certain that an earthquake will occur someday. What is the probability (to the nearest percent) that it will occur while you are at school? Assume you are at school 5 hours per day, 174
Prepare three cards that are identical except for the color. One card is black on both sides, one is white on both sides, and one is black on one side and white on the other.One side of one card is
Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome.If a seven or eleven occurs on the first roll, the player wins.a. What is the
In dice, a pair of ones is called snake eyes. What is the probability of losing a dice game by rolling snake eyes?
Consider a die with only four sides, marked one, two, three, and four.Figure 13.5a. Write out a sample space similar to the one in Figure 13.5 for rolling a pair of these dice.Assuming equally
The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked one, two, three, four, five, six, seven, and eight. Write a sample space similar to the one in Figure
A mad scientist has captured you and is showing you around his foul-smelling laboratory. He motions to an opaque, formal in filled jar. "This jar contains one organ, either a kidney or a brain," he
This question is to test your intuition. Read the following exercises (do not carry out the experiment).A. Open a phone book to any page in the white pages. Select 100 consecutive phone numbers and
True or false? In roulette, if you bet on black, the probability of winning is \(\frac{1}{2}\) because there are equal numbers of black and red spots. Explain.
True or false? An expected value of \(\$ 5\) means that you should expect to win \(\$ 5\) each time you play the game. Explain.
True or false? If the expected value of a game is positive, then it is a game you should play. Explain.
Suppose that you buy a lottery ticket for \(\$ 1\). The payoff is \(\$ 50,000\), with a probability of winning \(1 / 1,000,000\). Therefore, the expected value is\[E=\$
In Illinois, \(42.5 \%\) of all money wagered in the lottery must be returned in winnings. If you bet \(\$ 10\), does this mean that your expectation is \(\$ 4.25\) ?
If you were asked to choose between a sure \(\$ 10,000\), or an \(80 \%\) chance of winning \(\$ 15,000\) and a \(20 \%\) chance of winning nothing, which would you take?Game A:\[E=\$ 10,000(1)=\$
Use estimation to select the best response in Problems 7-12. Do not calculate.The expectation from playing a game in which you win \(\$ 950\) by correctly calling heads or tails when you flip a coin
Use estimation to select the best response in Problems 7-12. Do not calculate.The expectation from playing a game in which you win \(\$ 950\) by correctly calling heads or tails on each of five flips
Use estimation to select the best response in Problems 7-12. Do not calculate.If the expected value of playing a \(\$ 1\) game of blackjack is \(\$ 0.04\), then after playing the game 100 times you
Use estimation to select the best response in Problems 7-12. Do not calculate.If your expected value when playing a \(\$ 1\) game of roulette is \(-\$ 0.05\), then after playing the game 100 times
Use estimation to select the best response in Problems 7-12. Do not calculate.The probability of correctly guessing a telephone number is about A. 1 out of 100 B. 1 out of 1,000 C. 1 out of
Use estimation to select the best response in Problems 7-12. Do not calculate.Winning over \(\$ 10\) million in a super lottery is about as probable as A. having a car accident B. having an item fall
Suppose that you roll two dice. You will be paid \(\$ 5\) if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling
A magazine subscription service is having a contest in which the prize is \(\$ 80,000\). If the company receives 1 million entries, what is the expectation of the contest?
A box contains one each of \(\$ 1, \$ 5, \$ 10, \$ 20\), and \(\$ 100\) bills. You reach in and withdraw one bill. What is the expected value?
A box contains one each of \(\$ 1, \$ 5, \$ 10, \$ 20\), and \(\$ 100\) bills. It costs \(\$ 20\) to reach in and withdraw one bill. What is the expected value?
Suppose that you have 5 quarters, 5 dimes, 10 nickels, and 5 pennies in your pocket. You reach in and choose a coin at random so that you can give it to your child. What is the expectation? What is
A game involves tossing two coins and receiving \(50 otin\) if they are both heads. What is a fair price to pay for the privilege of playing?
Krinkles potato chips is having a "Lucky Seven Sweepstakes." The one grand prize is \(\$ 70,000 ; 7\) second prizes each pay \(\$ 7,000\); 77 third prizes each pay \(\$ 700\); and 777 fourth prizes
A punch-out card contains 100 spaces. One space pays \(\$ 100\), five spaces pay \(\$ 10\), and the others pay nothing. How much should you pay to punch out one space?
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Black 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17 34 6 27
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Odd 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17 34 6 27 13
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Single-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Double -number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure13.8Three-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Four-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Five-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Six-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Twelve-number bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25
What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8Column bet 4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17 34 6
Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is \(\$ 5.00\) and that you will receive the amount shown on the spinner
Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is \(\$ 5.00\) and that you will receive the amount shown on the spinner
Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is \(\$ 5.00\) and that you will receive the amount shown on the spinner
Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is \(\$ 5.00\) and that you will receive the amount shown on the spinner
Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed on the board. How much should you be willing to pay for the opportunity to
Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed on the board. How much should you be willing to pay for the opportunity to
In old gangster movies on TV, you often hear of "number runners" or the "numbers racket." This numbers game, which is still played today, involves betting \(\$ 1\) on the last three digits of the
In a TV game show, four prizes are hidden on a game board that contains 20 spaces. One prize is worth \(\$ 10,000\), two prizes are worth \(\$ 5,000\), and the other prize is worth \(\$ 1,000\). The
Suppose it costs \(\$ 2,400\) to advertise and list a \(\$ 350,000\) house for sale. The listing agent will earn \(5 \%\) of the selling price if the listing agent sells the property, but only \(2.5
A realtor who takes the listing on a house to be sold knows that she will spend \(\$ 800\) trying to sell the house. If she sells it herself, she will earn \(6 \%\) of the selling price. If another
An oil-drilling company knows that it costs \(\$ 25,000\) to sink a test well. If oil is hit, the income for the drilling company will be \(\$ 425,000\). If only natural gas is hit, the income will
In Problem 41, suppose that the income for hitting oil is changed to \(\$ 825,000\) and the income for gas to \(\$ 225,000\). Now what is the expectation for the drilling company? Should the company
Consider the following game in which a player rolls a single die. If a prime \((2,3\), or 5\()\) is rolled, the player wins \(\$ 2\). If a square ( 1 or 4 ) is rolled, the player wins \(\$ 1\).
A game involves drawing a single card from an ordinary deck. If an ace is drawn, you receive \(50 \phi\); if a face card is drawn, you receive \(25 \phi\); if the two of spades is drawn, you receive
A company held a contest, and the following information was included in the fine print:Read this information carefully, and calculate the expectation (to the nearest cent) for this contest. Prize
A company held a bingo contest for which the following chances of winning were given:What is the expectation (to the nearest cent) from playing one card 13 times? Playing One Card, Your Chances of
Heights (in inches) obtained by a group of people in a random survey are reported in the following table: Height 55 60 65 70 75 80 85 90 Probability 0.001 0.022 0.136 0.341 0.341 0.136 0.022 0.001
In a certain school, the probabilities of the number of students who are reported tardy are shown in the following table:What is the expected number of tardies (rounded to two decimal places)? Number
Calculate the expectation (to the nearest cent) for the Reader's Digest sweepstakes described. Assume there are 197,000,000 entries. $10,500,000.00 ENTRY DOCUMENT SWEEPSTAKES Official Disclosure of
A merchant is considering a purchase of autographed sports memorabilia for resale to collectors. The probabilities of various possible incomes from reselling these collectibles are estimated in the
Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win \(\$ 1\) million. The contestant picks from four hidden windows. Behind each is
Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win \(\$ 1\) million. The contestant picks from four hidden windows. Behind each is
Suppose you are in class and your instructor makes you the following legitimate offer. Each student receives a ballot with the following two choices, without communicating with each other:If everyone
Repeat Problem 53, except change the stakes to \(\$ 110\) and \(\$ 100\), respectively.Data from problem 53Suppose you are in class and your instructor makes you the following legitimate offer. Each
Repeat Problem 53, except change the stakes to \(\$ 10,000\) and \(\$ 10\), respectively.Data from problem 53Suppose you are in class and your instructor makes you the following legitimate offer.
Repeat Problem 53, except change the stakes to be an A grade in the class if everyone checks the first box, but if anyone checks the second box, the following will occur: Those who check it will have
The Swiss mathematician Daniel Bernoulli (1700-1782) was part of the famous Bernoulli family . In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St.
The Swiss mathematician Daniel Bernoulli (1700-1782) was part of the famous Bernoulli family . In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St.
The Swiss mathematician Daniel Bernoulli (1700-1782) was part of the famous Bernoulli family . In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St.
The Swiss mathematician Daniel Bernoulli (1700-1782) was part of the famous Bernoulli family . In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St.
What is the fundamental counting principle?
Explain what we mean by "conditional probability."
What is the birthday problem?
Compare and contrast odds and probability.
Use estimation to select the best response in Problems 5-10. Do not calculate.Of these three means of travel, the safest is A. car B. train C. plane
Use estimation to select the best response in Problems 5-10. Do not calculate.Which of the following is a conditional probability?A. \(P(\) normal female \()\)B. \(P(\bar{A})\)C. \(P(\) normal
Use estimation to select the best response in Problems 5-10. Do not calculate.Which of the following is more probable?A. Flipping a coin 3 times and obtaining at least 2 heads B. Flipping a coin 4
Use estimation to select the best response in Problems 5-10. Do not calculate.Which of the following is more probable?A. Rolling a die 3 times and obtaining a six 2 times B. Rolling a die 3 times and
Use estimation to select the best response in Problems 5-10. Do not calculate.Which of the following is more probable?A. Correctly guessing all the answers on a 20-question true-false examination B.
Use estimation to select the best response in Problems 5-10. Do not calculate.Which of the following is more probable?A. Correctly guessing all the answers on a 10-question 5-part multiple-choice
Find the requested probabilities in Problems 11-14.\(P(\bar{A})\) if \(P(A)=0.6\)
Find the requested probabilities in Problems 11-14.\(P(\bar{B})\) if \(P(B)=\frac{4}{5}\)
Find the requested probabilities in Problems 11-14.\(P(C)\) if \(P(\bar{C})=\frac{9}{13}\)
Find the requested probabilities in Problems 11-14.\(P(D)\) if \(P(\bar{D})=0.005\)
A card is selected from an ordinary deck. What is the probability that it is not a face card?
Choose a natural number between 1 and 100, inclusive. What is the probability that the number chosen is not a multiple of 5 ?

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