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# rec03-1 - Massachusetts Institute of Technology Department...

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Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2008) Recitation 3 September 11, 2008 1. A coin is tossed four times independently. The probability of heads at each toss is p . Let A be the event that the first and second tosses result in heads. Let B be the event that the second and third tosses result in heads. Let C be the event that the third and fourth tosses result in heads. (a) Are the events A and B independent? (b) Are the events A and C independent? Do your answers depend on p ? 2. Do longer games favor the stronger player? What does “stronger player” mean? 1 Turtle and Hare compete in a game that may have multiple independent rounds, where the player with highest total score wins. Turtle scores 2 points in every round, while Hare scores 3 points with probability p or 0 points with probability 1 - p . (a) What is the probability Hare wins a two-round game?

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rec03-1 - Massachusetts Institute of Technology Department...

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