Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Chapter 13.1, Problem 44PS
Suppose you and an opponent each pick one of the spinners shown here. A”win” means spinning a higher number. Construct a
E plays F. 
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Chapter 13 Solutions
Nature of Mathematics (MindTap Course List)
Ch. 13.1 - IN YOUR OWN WORDS What is the difference between...Ch. 13.1 - IN YOUR OWN WORDS Define probabilities?Ch. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...
Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Prob. 12PSCh. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Poker is a common game in which players are dealt...Ch. 13.1 - Prob. 16PSCh. 13.1 - Prob. 17PSCh. 13.1 - Prob. 18PSCh. 13.1 - Prob. 19PSCh. 13.1 - Prob. 20PSCh. 13.1 - Prob. 21PSCh. 13.1 - Some numbers are shown in Table 13.1. Explain...Ch. 13.1 - a. One airline has six across seating in coach. If...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - A single card is selected from an ordinary deck of...Ch. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Prob. 29PSCh. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Suppose that you toss a coin and roll a die in...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Prob. 33PSCh. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Prob. 35PSCh. 13.1 - Prob. 36PSCh. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Use the sample space shown in Figure 13.5 to find...Ch. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Prob. 42PSCh. 13.1 - Prob. 43PSCh. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Prob. 45PSCh. 13.1 - Prob. 46PSCh. 13.1 - Suppose you and an opponent each pick one of the...Ch. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Prob. 49PSCh. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Perform the experiments in Problems 48-51, tally...Ch. 13.1 - Prob. 52PSCh. 13.1 - Suppose it is certain that an earthquake will...Ch. 13.1 - Dice is a popular game in gambling casinos. Two...Ch. 13.1 - In dice, a pair of ones is called snake eyes. What...Ch. 13.1 - Consider a die with only four sides, marked one,...Ch. 13.1 - The game of Dungeons and Dragons uses nonstandard...Ch. 13.1 - A mad scientist has captured you and is showing...Ch. 13.2 - Level 1 IN YOUR OWN WORDS True or false? In...Ch. 13.2 - Level 1 IN YOUR OWN WORDS True or false? An...Ch. 13.2 - Prob. 3PSCh. 13.2 - Prob. 4PSCh. 13.2 - Prob. 5PSCh. 13.2 - Prob. 6PSCh. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Prob. 9PSCh. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Use estimation to select the best response...Ch. 13.2 - Level 1 Suppose that you roll two dice. You will...Ch. 13.2 - Level 1 A magazine subscription service is having...Ch. 13.2 - Level 1 A box contains one each of 1,5,10,20, and...Ch. 13.2 - Level 1 A box contains one each of 1,5,10,20, and...Ch. 13.2 - Level 1 Suppose that you have 5 quarters, 5 dimes,...Ch. 13.2 - Level 1 A game involves tossing two coins and...Ch. 13.2 - Level 1 Krinkles potato chips is having a Lucky...Ch. 13.2 - Level 1 A punch-out card contains 100 spaces. One...Ch. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 22PSCh. 13.2 - Prob. 23PSCh. 13.2 - Prob. 24PSCh. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 26PSCh. 13.2 - Prob. 27PSCh. 13.2 - Level 2 What is the expectation for the 1 bets in...Ch. 13.2 - Prob. 29PSCh. 13.2 - Prob. 30PSCh. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Prob. 32PSCh. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Level 2 Consider the spinners in Problems 31-34....Ch. 13.2 - Level 2 Assume that a dart is randomly thrown at...Ch. 13.2 - Level 2 Assume that a dart is randomly thrown at...Ch. 13.2 - Level 2 In old gangster movies on TV, you often...Ch. 13.2 - Prob. 38PSCh. 13.2 - Prob. 39PSCh. 13.2 - Level 2 A realtor who takes the listing on a house...Ch. 13.2 - Level 2 An oil-drilling company knows that it...Ch. 13.2 - Level 2 In Problem 41, suppose that the income for...Ch. 13.2 - Level 2 Consider the following game in which a...Ch. 13.2 - Level 2 A game involves drawing a single card from...Ch. 13.2 - Level 2 A company held a contest, and the...Ch. 13.2 - Level 2 A company held a bingo contest for which...Ch. 13.2 - Level 2 Heights in inches obtained by a group of...Ch. 13.2 - Level 2 In a certain school, the probabilities of...Ch. 13.2 - Level 2 Calculate the expectation to the nearest...Ch. 13.2 - Prob. 50PSCh. 13.2 - Prob. 51PSCh. 13.2 - Prob. 52PSCh. 13.2 - Prob. 53PSCh. 13.2 - Prob. 54PSCh. 13.2 - Prob. 55PSCh. 13.2 - Prob. 56PSCh. 13.2 - Problem Solving Level 3 HISTORICAL QUEST The Swiss...Ch. 13.2 - Problem Solving Level 3 HISTORICAL QUEST The Swiss...Ch. 13.2 - Prob. 59PSCh. 13.2 - Prob. 60PSCh. 13.3 - IN YOUR OWN WORDS What is the fundamental counting...Ch. 13.3 - Prob. 2PSCh. 13.3 - Prob. 3PSCh. 13.3 - Prob. 4PSCh. 13.3 - Prob. 5PSCh. 13.3 - Prob. 6PSCh. 13.3 - Which of the following is more probable? A....Ch. 13.3 - Prob. 8PSCh. 13.3 - Which of the following is more probable? A....Ch. 13.3 - Prob. 10PSCh. 13.3 - Find the requested probabilities in Problems...Ch. 13.3 - Prob. 12PSCh. 13.3 - PC ifPC-=913Ch. 13.3 - Prob. 14PSCh. 13.3 - Prob. 15PSCh. 13.3 - Choose a natural number between 1 and 100,...Ch. 13.3 - Three fair coins are tossed. What is the...Ch. 13.3 - Find the probability of obtaining at least one...Ch. 13.3 - What are the odds in favor of drawing an ace from...Ch. 13.3 - What are a four-child familys odds against having...Ch. 13.3 - The probability of drawing a heart from a deck of...Ch. 13.3 - Suppose the probability of an event is 0.80. What...Ch. 13.3 - Prob. 23PSCh. 13.3 - Racetracks quote the approximate odds for each...Ch. 13.3 - Prob. 25PSCh. 13.3 - Suppose the odds are 33 to 1 that someone will lie...Ch. 13.3 - 27. Suppose that a family want to have four...Ch. 13.3 - Prob. 28PSCh. 13.3 - Prob. 29PSCh. 13.3 - Prob. 30PSCh. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - Prob. 34PSCh. 13.3 - Prob. 35PSCh. 13.3 - A single card is drawn from a standard deck of...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Prob. 40PSCh. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - Two cards are drawn from a standard deck of cards,...Ch. 13.3 - What is the probability of getting a license plate...Ch. 13.3 - What is the probability of getting a license plate...Ch. 13.3 - 45. Consider the following table showing the...Ch. 13.3 - 46. Suppose a single die is rolled. Find the...Ch. 13.3 - Prob. 47PSCh. 13.3 - Prob. 48PSCh. 13.3 - 49. Suppose a pair of dice is rolled. Consider the...Ch. 13.3 - 50. Suppose a pair of dice is rolled. Consider the...Ch. 13.3 - Prob. 51PSCh. 13.3 - Show that the odds against an event E can be found...Ch. 13.3 - Prob. 53PSCh. 13.3 - A sorority has 35 members, 25 of whom are full...Ch. 13.3 - IN YOUR OWN WORDS The odds against winning a...Ch. 13.3 - Prob. 57PSCh. 13.3 - Prob. 58PSCh. 13.3 - Prob. 60PSCh. 13.4 - IN YOUR OWN WORDS What do we mean by independent...Ch. 13.4 - What is the formula for the probability of an...Ch. 13.4 - Prob. 3PSCh. 13.4 - Prob. 4PSCh. 13.4 - Prob. 5PSCh. 13.4 - Prob. 6PSCh. 13.4 - Prob. 7PSCh. 13.4 - Prob. 8PSCh. 13.4 - Prob. 9PSCh. 13.4 - Prob. 10PSCh. 13.4 - Suppose events A, B, and C are independent and...Ch. 13.4 - Suppose events A, B, and C are independent and...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - Prob. 16PSCh. 13.4 - Prob. 17PSCh. 13.4 - In Problems 13-24, suppose a die is rolled twice...Ch. 13.4 - Prob. 19PSCh. 13.4 - Prob. 20PSCh. 13.4 - Prob. 21PSCh. 13.4 - Prob. 22PSCh. 13.4 - Prob. 23PSCh. 13.4 - Prob. 24PSCh. 13.4 - Prob. 25PSCh. 13.4 - Prob. 26PSCh. 13.4 - Prob. 27PSCh. 13.4 - Prob. 28PSCh. 13.4 - Prob. 29PSCh. 13.4 - Prob. 30PSCh. 13.4 - Prob. 31PSCh. 13.4 - Prob. 32PSCh. 13.4 - Prob. 33PSCh. 13.4 - Prob. 34PSCh. 13.4 - Prob. 35PSCh. 13.4 - Prob. 36PSCh. 13.4 - A certain slot machine has three identical...Ch. 13.4 - Suppose slot machine has three identical...Ch. 13.4 - Prob. 39PSCh. 13.4 - The one coin payoffs for the slot machine shown in...Ch. 13.4 - A high rollers Keno is offered in which you pay...Ch. 13.4 - A special catch all Keno ticket allows you to play...Ch. 13.4 - What is the expectation for playing Keno by...Ch. 13.4 - What is the expectation for playing a four-spot...Ch. 13.4 - What is the probability of obtaining five tails...Ch. 13.4 - Prob. 46PSCh. 13.4 - Assume a jar has five red marbles and three black...Ch. 13.4 - Suppose that in an assortment of 20 calculators...Ch. 13.4 - a. A game consists of at most three cuts with a...Ch. 13.4 - Prob. 50PSCh. 13.4 - Prob. 51PSCh. 13.4 - Prob. 52PSCh. 13.4 - Prob. 53PSCh. 13.4 - Prob. 54PSCh. 13.4 - Prob. 55PSCh. 13.4 - Prob. 56PSCh. 13.4 - Prob. 57PSCh. 13.4 - Prob. 58PSCh. 13.4 - Prob. 59PSCh. 13.4 - Prob. 60PSCh. 13.5 - Prob. 1PSCh. 13.5 - Prob. 2PSCh. 13.5 - Prob. 3PSCh. 13.5 - Prob. 4PSCh. 13.5 - Prob. 5PSCh. 13.5 - Prob. 6PSCh. 13.5 - Prob. 7PSCh. 13.5 - Prob. 8PSCh. 13.5 - Prob. 9PSCh. 13.5 - Prob. 10PSCh. 13.5 - Prob. 11PSCh. 13.5 - Prob. 12PSCh. 13.5 - Prob. 13PSCh. 13.5 - Prob. 14PSCh. 13.5 - Prob. 15PSCh. 13.5 - Prob. 16PSCh. 13.5 - Prob. 17PSCh. 13.5 - Prob. 18PSCh. 13.5 - Prob. 19PSCh. 13.5 - Prob. 20PSCh. 13.5 - Prob. 21PSCh. 13.5 - Prob. 22PSCh. 13.5 - Prob. 23PSCh. 13.5 - Prob. 24PSCh. 13.5 - Prob. 25PSCh. 13.5 - Prob. 26PSCh. 13.5 - Prob. 27PSCh. 13.5 - Prob. 28PSCh. 13.5 - Prob. 29PSCh. 13.5 - Prob. 30PSCh. 13.5 - Prob. 31PSCh. 13.5 - Prob. 32PSCh. 13.5 - Prob. 33PSCh. 13.5 - Prob. 34PSCh. 13.5 - Prob. 35PSCh. 13.5 - Prob. 36PSCh. 13.5 - Prob. 37PSCh. 13.5 - Prob. 38PSCh. 13.5 - Prob. 39PSCh. 13.5 - Prob. 40PSCh. 13.5 - Prob. 41PSCh. 13.5 - Prob. 42PSCh. 13.5 - Prob. 43PSCh. 13.5 - Prob. 44PSCh. 13.5 - Prob. 45PSCh. 13.5 - Prob. 46PSCh. 13.5 - Prob. 47PSCh. 13.5 - Prob. 48PSCh. 13.5 - Prob. 49PSCh. 13.5 - Prob. 50PSCh. 13.5 - Suppose the people in a room are divided into two...Ch. 13.5 - Prob. 52PSCh. 13.5 - Prob. 53PSCh. 13.5 - Prob. 54PSCh. 13.5 - Prob. 55PSCh. 13.5 - Prob. 56PSCh. 13.5 - Prob. 57PSCh. 13.5 - Prob. 58PSCh. 13.5 - Prob. 59PSCh. 13.5 - Prob. 60PSCh. 13.6 - Level 1. IN YOUR OWN WORDS What is a binomial...Ch. 13.6 - Prob. 2PSCh. 13.6 - Level 1. Find the binomial probabilities in...Ch. 13.6 - Prob. 4PSCh. 13.6 - Prob. 5PSCh. 13.6 - Prob. 6PSCh. 13.6 - Prob. 7PSCh. 13.6 - Prob. 8PSCh. 13.6 - Prob. 9PSCh. 13.6 - Prob. 10PSCh. 13.6 - Level 1. Find the probability of obtaining exactly...Ch. 13.6 - Prob. 12PSCh. 13.6 - Prob. 13PSCh. 13.6 - Prob. 14PSCh. 13.6 - Prob. 15PSCh. 13.6 - Prob. 16PSCh. 13.6 - Prob. 17PSCh. 13.6 - Prob. 18PSCh. 13.6 - Prob. 19PSCh. 13.6 - Prob. 20PSCh. 13.6 - Prob. 21PSCh. 13.6 - Prob. 22PSCh. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Prob. 25PSCh. 13.6 - Level 1. Suppose a jar contains 3 pens: 1 red, 1...Ch. 13.6 - Prob. 27PSCh. 13.6 - Prob. 28PSCh. 13.6 - Prob. 29PSCh. 13.6 - Prob. 30PSCh. 13.6 - Prob. 31PSCh. 13.6 - Prob. 32PSCh. 13.6 - Prob. 33PSCh. 13.6 - Prob. 34PSCh. 13.6 - Prob. 35PSCh. 13.6 - Prob. 36PSCh. 13.6 - Prob. 37PSCh. 13.6 - Prob. 38PSCh. 13.6 - Prob. 39PSCh. 13.6 - Prob. 40PSCh. 13.6 - Level 2. What is the probability that if a pair of...Ch. 13.6 - Level 2. What is the probability that if a pair of...Ch. 13.6 - Prob. 43PSCh. 13.6 - Prob. 44PSCh. 13.6 - Prob. 45PSCh. 13.6 - Prob. 46PSCh. 13.6 - Prob. 47PSCh. 13.6 - Prob. 48PSCh. 13.6 - Prob. 49PSCh. 13.6 - Prob. 50PSCh. 13.6 - Prob. 51PSCh. 13.6 - Prob. 52PSCh. 13.6 - Prob. 53PSCh. 13.6 - Prob. 54PSCh. 13.6 - Prob. 55PSCh. 13.6 - Prob. 56PSCh. 13.6 - Prob. 57PSCh. 13.6 - Prob. 58PSCh. 13.6 - Prob. 59PSCh. 13.6 - Prob. 60PSCh. 13.CR - Prob. 1CRCh. 13.CR - Prob. 2CRCh. 13.CR - Prob. 3CRCh. 13.CR - Prob. 4CRCh. 13.CR - Prob. 5CRCh. 13.CR - Prob. 6CRCh. 13.CR - Prob. 7CRCh. 13.CR - Prob. 8CRCh. 13.CR - Prob. 9CRCh. 13.CR - Prob. 10CRCh. 13.CR - Prob. 11CRCh. 13.CR - Prob. 12CRCh. 13.CR - Prob. 13CRCh. 13.CR - Prob. 14CRCh. 13.CR - The probability that an individual who is selected...Ch. 13.CR - Prob. 16CRCh. 13.CR - Prob. 17CRCh. 13.CR - Prob. 18CRCh. 13.CR - Prob. 19CRCh. 13.CR - Prob. 20CR
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- 2 (VaR and ES) Suppose X1 are independent. Prove that ~ Unif[-0.5, 0.5] and X2 VaRa (X1X2) < VaRa(X1) + VaRa (X2). ~ Unif[-0.5, 0.5]arrow_forward8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.arrow_forward9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.arrow_forward
- 7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forward(^) k Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as n! k! (n−k)! Question 1. (1) Prove the following identity: (22) + (1121) = (n+1). (2) Use the identity above to prove the binomial theorem by induction. That is, prove that for any a, b = R, n (a + b)" = Σ (^) an- n-kyk. k=0 n Recall that Σ0 x is short hand notation for the expression x0+x1+ +xn- (3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using the binomial theorem. - Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y. Question 3. Assume (In) nEN is a sequence which is unbounded above. That is, the set {xn|nЄN} is unbounded above. Prove that there are natural numbers N] k for all k Є N. be natural numbers (nk Є N). Prove thatarrow_forward
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