Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 2 September 14, 2010 1. 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 know that the Frst 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 di±erence 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 equally likely. (a) ²ind the probability that doubles are rolled. (b) Given that the roll results in a sum of 4 or less, Fnd the conditional probability that doubles are rolled. (c) ²ind the probability that at least one die roll is a 6. (d) Given that the two dice land on di±erent numbers, Fnd the conditional probability that at least one die roll is a 6. 3. Example 1.13, page 29, and Example 1.17, page 33, in the text.
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This note was uploaded on 12/02/2011 for the course ENGINEERIN EE302 taught by Professor Proasin during the Spring '11 term at South Carolina.