The Art of Probability

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Content: Cover Half Title Title Page Copyright Page Preface Table of Contents References Chapter 1: Probability 1.1 Introduction 1.2 Models in General 1.3 The Frequency Approach Rejected 1.4 The Single Event Model 1.5 Symmetry as the Measure of Probability 1.5-1 Selected faces of a die 1.5-2 A card with the face 7 1.5-3 Probability of a spade 1.6 Independence 1.6-1 The sample space of two dice 1.6-2 The sample space of three coins 1.6-3 The number of paths 1.7 Subsets of a Sample Space 1.7-1 Exactly one head in three tosses of three coins 1.7-2 Sum of two dice. Aside: Probability scales1.8 Conditional Probability 1.8-1 At least two heads in ten tosses 1.8-2 An even sum on two dice 1.8-3 Probability of exactly three heads given that there are at least two heads 1.9 Randomness 1.9-1 The two gold coin problem 1.9-2 The two children problem 1.9-3 The four card deck 1.9-4 The two headed coin 1.9-5 No information 1.9-6 The birthday problem 1.9-7 The general case of coincidences 1.9-8 The information depends on your state of knowledge 1.10 Critique of the Model 1.A Bounds on Sums 1.B A Useful Bound Chapter 2: Some Mathematical Tools. 2.1 Introduction2.2 Permutations 2.2-1 Arrange 3 books on a shelf 2.2-2 Arrange 6 books on a shelf 2.2-3 Arrange 10 books on a shelf 2.2-4 Two out of three items identical 2.2-5 Another case of identical items 2.3 Combinations 2.3-1 Sums of binomial coefficients 2.3-2 Bridge hands 2.3-3 3 out of 7 books 2.3-4 Probability of n heads in 2n tosses of a coin 2.3-5 Probability of a void in bridge 2.3-6 Similar items in bins 2.3-7 With at least 1 in each bin 2.4 The Binomial Distributionâ#x80 #x93 Bernoulli Trials 2.4-1 Inspection of parts 2.4-2 Continued 2.4-3 Floppy discs. 2.4-4 Distribution of the sum of three dice2.4-5 Bose-Einstein statistics 2.4-6 Fermi-Dirac statistics 2.5 Random Variables, Mean and the Expected Value 2.5-1 Expected value of a roll of a die 2.5-2 Expected value of a coin toss 2.5-3 Sum of two dice 2.5-4 Gambling on an unknown bias Mathematical aside: Sums of powers of the integers 2.6 The Variance 2.6-1 Variance of a die 2.6-2 Variance of M equally likely outcomes 2.6-3 Variance of the sum of n dice 2.7 The Generating Function 2.7-1 Mean and variance of the binomial distribution 2.7-2 The binomial distribution again. 2.7-3 The distribution of the sum of three dice2.8 The Weak Law of Large Numbers 2.9 The Statistical Assignment of Probability 2.9-1 Test of coin and Monte Carlo methods 2.9-2 Chevalier de Mere problem 2.10 The Representation of Information 2.11 Summary 2.A Derivation of the Weak Law of Large Numbers 2.B Useful Binomial Identities Chapter 3: Methods for Solving Problems 3.1 The Five Methods 3.1-1 The elevator problem (five ways) 3.2 The Total Sample Space and Fair Games 3.2-1 Matching pennies (coins) 3.2-2 Biased coins 3.2-3 Raffles and lotteries.