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MIT6_041F10_assn01

# MIT6_041F10_assn01 - Massachusetts Institute of Technology...

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Page 1 of 2 Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Spring 2010) Problem Set 1 Due: September 15, 2010 1. Express each of the following events in terms of the events A , B and C as well as the operations of complementation, union and intersection: (a) at least one of the events A , B , C occurs; (b) at most one of the events A , B , C occurs; (c) none of the events A , B , C occurs; (d) all three events A , B , C occur; (e) exactly one of the events A , B , C occurs; (f) events A and B occur, but not C ; (g) either event A occurs or, if not, then B also does not occur. In each case draw the corresponding Venn diagrams. 2. You ﬂip a fair coin 3 times, determine the probability of the below events. Assume all sequences are equally likely. (a) Three heads: HHH (b) The sequence head, tail, head: HTH (c) Any sequence with 2 heads and 1 tail (d) Any sequence where the number of heads is greater than or equal to the number of tails 3. Bob has a peculiar pair of four-sided dice.

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MIT6_041F10_assn01 - Massachusetts Institute of Technology...

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