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# 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

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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 f 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

1. (a) Probability of obtaining 1 or 4 = 2/6= 1/3
(b) Probability of obtaining even = 3/6= ½
2. (a) Either 7,1 or 1,7 will have a 7
So P= 2/36 = 1/18
(b) P = 27/36 = ¾
3. a) P =...

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