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# hw1 - Middle East Technical University Department of...

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Middle East Technical University Department of Electrical and Electronics Engineering EE230: Probability and Random Variables Homework 1 Due: October 12, 2012, 17:30 1) Emre and Selin attend probability lectures randomly and independently. Any lecture is equally likely to be attended by each of them. Emre attends exactly one of the three lectures and Selin attends exactly two of them each week. a) Construct a sample space for this experiment. b) Find the probability that they meet at a lecture. 2) A fair die is rolled. According to the outcome of die rolling, a ball is drawn from the six boxes numbered as 1, 2, 3, 4, 5, 6 each one containing k black and 6-k red balls where k is the box number. a) What is the probability of picking a red ball? b) If it is known that a red all is drawn, what is the probability that die rolling resulted in 4? c) If it is known that a red ball is drawn and then it is placed back into its box. Now we draw another ball from the same box. What is the probability that it is red again?
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