# hw2 - B.1 What is the probability that someone who tests...

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Computer Science 340 Reasoning about Computation Homework 2 Due at the beginning of class on Wednesday, October 3, 2007 Problem 1 Consider a convex n -gon (a polygon with n sides). A chord is a line segment between two non-adjacent vertices. If all chords are drawn, in how many interior points do they intersect? (Assume no three chords intersect at the same point.) Problem 2 Let S = { 1 , 2 , ..., n } . How many ordered pairs ( A, B ) of subsets of S are there that satisfy A B ? Problem 3 (A) Box 1 contains 2 white balls and 3 blue balls. Box 2 contains 4 white balls and 1 blue ball. If you pick a box at random and then a ball at random from that box, what is the probability that you pick a ball from the first box if you end up with a blue ball (ie, conditioned upon the outcome that you take a blue ball)? (B) A test for steroids has a 2% false positive rate and a 5% false negative rate. This means that 2% of ball players who do not take steroids test positive for them, and 5% of the steroid users test negative. Suppose that 1% of players use steroids:
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Unformatted text preview: B.1 What is the probability that someone who tests positive actually uses steroids? B.2 What is the probability that someone who tests negative does not use steroids? Problem 4 The publicity team for the next Harry Potter movie makes the following deal with Coca-Cola: Every Coke bottle has a picture of a character from the movie on the bottom of the cover. There are n characters in all, and you want to collect one picture of each. (Assume that each bottle has a picture of a character chosen uniformly at random from the n possible characters, independent of other bottles). 1. Suppose that you have already collected pictures of k characters. What is the expected number of additional bottles you must drink to collect one additional character? 2. What is the expected number of bottles that you must drink to collect all pictures of all n characters?...
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