Hw1-2011 - Theory of Probability HW#1 all sections Assignment Date March 4 2011 Due Date March 11,2011 1 The game of craps is played as follows A

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Unformatted text preview: Theory of Probability, HW #1, all sections Assignment Date: March 4, 2011; Due Date: March 11,2011 1. The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a 2, 3, or 12, the player loses; if the sum is either a 7 or an 11, he or she wins. If the outcome is anything else, the player continues to roll the dice until he or she rolls either the initial outcome or a 7. If the 7 comes first, the player loses; whereas if the initial outcome reoccurs before the 7, the player wins. Compute the probability of a player winning at craps. Hint : Let g G denote the event that the initial outcome is i and the player wins. The desired probability is ∑ ¡(g G ) ¢£ G¤£ . To compute ¡(g G ), define the events g G,¥ to be the event that the initial sum is i and the player wins on the n th roll. Argue that ¡(g G ) = ∑ ¡¦g G,¥ § ∞ ¥¤¢ . 2. We have a stick of 9 consecutive parts. Each part is painted red or white. If none of the neighboring parts are painted white, how We have a stick of 9 consecutive parts....
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This note was uploaded on 05/12/2011 for the course INDUSTRIAL 321 taught by Professor Memet during the Spring '11 term at Mitchell Technical Institute.

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