PS02 - University of Illinois Spring 2010 ECE 313 Problem...

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University of Illinois Spring 2010 ECE 313: Problem Set 2 Due: Wednesday, February 3rd at 4 p.m. Reading I: Ross, Chapter 1, Sections 1-6, and Chapter 2, Sections 1-7 Reading II: Lecture Notes 2-6 Noncredit Exercises: DO NOT turn these in. Chapter 1: Problems 1-5, 7, 9; Theoretical Exercises 4, 6, 13; Self-Test Problems 1-15. Chapter 2: Problems 3, 4, 9, 10,11-14; Theoretical Exercises 1-3, 6, 10, 11, 16, 19, 20; Self-Test Problems 1-8 This Problem Set contains seven problems. The problems give you practice in counting and in the calculation of probabilities using the axioms of probability. 1. Each morning, before they go off to work in the mines, the seven dwarves line up and Snow White kisses each dwarf on the top of his head. In order to avoid any hint of favoritism, she kisses them in random order each morning. (a) What is the probability that the dwarf named Bashful gets kissed first on Mon- day? (b) What is the probability that Bashful gets kissed first both Monday and Tuesday? (c) What is the probability that Bashful does not get kissed first, either Monday or Tuesday? (d) What is the probability that Bashful gets kissed first at least once during the week (Monday Friday)? 2. Alice and Bob roll a standard die obtaining a number at random from 1 to 6. What is the probability that Alices number is larger than Bobs number? What is the probability that Alice’s number is by one larger than Bob’s number?
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