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4204hw4 - 1 A classic joke about theoretical physicists...

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Combinatorics II (MAD 4204) — Spring 2011 Due Friday 2/25/2011 Homework #4 1 Prove that any two-coloring of the edges of K 6 contains a monochromatic quadrilateral (i.e., a 4-vertex cycle all of whose edges are the same color). 2 Exercise #22 in Chapter 15 states: “What is the probability that two people in a group of six were born in the same month of the year?” (a.) Give a “spherical cow” 1 solution to this problem. (b.) Identify at least two factors that make your answer above inaccurate. 3 Is it true that if the occurrence of event A makes event B more likely, then the occurrence of B makes A more likely? Prove or give a counterexample. 4 Suppose you roll a standard 6-sided die five times, recording each number you roll. What is the probability that this sequence is monotone increasing?
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Unformatted text preview: 1 A classic joke about theoretical physicists, stolen from Wikipedia, goes as follows. Milk production at a dairy farm was low so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer “I have the solution, but it only works for spherical cows in a vacuum.”...
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