Massachusetts Institute of TechnologyDepartment of Electrical Engineering & Computer Science6.041/6.431: Probabilistic Systems Analysis(Fall 2010)Recitation 2September 14, 20101. Problem 1.15, page 56-57 in the text.A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we knowthat the first toss is a head than if we know that at least one of the tosses is a head. Is she right?Does it make a difference if the coin is fair or unfair? How can we generalize Alice’s reasoning?2. Problem 1.14, page 56 in the text.We roll two fair 6-sided dice.Each one of the 36 possible outcomes is assumed to be equallylikely.(a) Find the probability that doubles are rolled.(b) Given that the roll results in a sum of 4 or less, find the conditional probability that doublesare rolled.(c) Find the probability that at least one die roll is a 6.(d) Given that the two dice land on different numbers, find the conditional probability that atleast one die roll is a 6.
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