11ProbHw2 - IEOR 3658 Probability Prof. Mariana...

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IEOR 3658 Assignment #2 Probability September 21, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #2 – due September 28th, 2011 1. You have 3 coins in your pocket that are undistinguishable to the touch; two of them are normal coins, the other one has “heads” on both sides. Suppose you take a coin out of your pocket at random, toss it, and obtain a “head”. What is the probability that the coin you tossed is the double-headed one? 2. Three urns are filled with a mixture of green and white balls that are undistinguishable to the touch, as follows: urn no. 1: three green balls, nine white balls; urn no. 2: four green balls, eight white balls; urn no. 3: six green balls, six white balls. By a suitable procedure that does not favor any one urn, the experimenter chooses one of the urns. Then she blindly picks a ball from the chosen urn. (a) What is the probability that the ball obtained in this manner is green? (b) If a green ball is picked, what is the probability that it came from urn no. 1?
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11ProbHw2 - IEOR 3658 Probability Prof. Mariana...

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