Question: MATH 645 Graph Theory Professor Narayan Homework Assignment: Due Monday, November 22, 2015 Be sure to show all of your work and fully justify all

MATH 645 Graph Theory Professor Narayan Homework Assignment: Due Monday, November 22, 2015 Be sure to show all of your work and fully justify all of your answers. 1. Suppose a single die is rolled. (a) What is the probability of obtaining a 1 or a 4? (b) What is the probability of obtaining an even number? 2. Suppose a pair of dice are rolled. (a) What is the probability of obtaining a 7? (b) What is the probability of obtaining an even number? (c) What is the probability of obtaining "doubles" (a pair of the same number)? 3. Suppose a die is rolled 100 times. (a) What is the probability of obtaining 36 fours? (b) What is the probability of obtaining at least 98 ves? 4. 5. How many ordered pairs of integers ( ) are needed to guarantee that there are two ordered pairs of (1 1 ) and (2 2 ) such that 1 mod 5 2 mod 5 and 1 mod 7 2 mod 7? Justify your answer. 1

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