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Unformatted text preview: ECE316 Additional Tutorial for the week of June 15 Problems from Textbook 8 th Edition Chapter 4 Page 172 Problem 4.1: Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings. What are the possible values of X , and what are the probabilities associated with each value? Solution: Assume that selecting the orange ball will not affect winning or losing. Selecting 2 balls out of 8+4+2 = 14 total balls, we will have a total number of combinations of g 14 2 G The possible values of X are : Balls selected Value of X Number of combinations 2 black 4 g 4 2 G 1 black & 1 orange 2 g 4 1 G g 2 1 G 1 black & 1 white 1 g 4 1 G g 8 1 G 2 orange 0 g 2 2 G 1 orange & 1 white 1 g 8 1 G g 2 1 G 2 white 2 g 8 2 G c The associated probabilities of different values of X = 4 = g 4 2 G g 14 2 G = 6 91 , = 2 = g 4 1 G g 2 1 G g 14 2 G = 8 91 = 1 = g 4 1 G g 8 1 G g 14 2 G = 32 91 , = 0 = g 2 2 G g 14 2 G = 1 91 = 1 = g 8 1 G g 2 1 G g 14 2 G = 16 91 , = 2 = g 8 2 G g 14 2 G = 28 91 Problem 4.2: Two fair dice are rolled. Let X equal the product of the 2 dice, compute gG = for = 1,2, ,36 Solution: 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36 The corresponding probabilities will be Value of X Number of occurrences Associated probability Value of X Number of occurrences Associated probability 1 1 1 36 23 0 36 2 2 2 36 24 2 2 36 3 2 2 36 25 1 1 36 4 3 3 36 26 0 36 5 2 2 36 27 0 36 6 4 4 36 28 0 36 7 0 36 29 0 36 8 2 2 36 30 2 2 36 9 1 1 36 31 0 36 10 2 2 36 32 0 36 11 0 36 33 0 36 12 4 4 36 34 0 36...
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 Spring '09
 Karnik
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