I first wrote this with a total word count of 60529 words, exceeding the 32000 limit. Here is PAR I. A separate topic will contain PART II. PART I 1. PROLOGUE 1.1 Lotteries & Probabilities John won a lottery, and the chance of winning was 1 in 100 million. Dale claims he can prove John cheated with the formula: [ P = 1 - (1 - p)^n ]. This calculates the probability of winning the lottery at least once with a given number of tickets [ n ]. Since [ p = \frac{1}{100,000,000} ]. Dale calculates ...