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Unformatted text preview: Math 210 — Topics in Finite Math
Spring 2007 — Midterm 1 Name: TA: VERSION B a)» The exam has 5 problems. (
(b) Show your work for every problem. Answers Without justiﬁcation Will not receive credit.
(c) Calculators are not allowed.  (d) There is a blank page at the end of the exam for if you need it.  1. (20 points) Let S be a sample space, and suppose E and F are events. (a) If Pr[E] = 0.4, Pr[F] = 0.6 and Pr[E U P] = 0.7, what is Pr[E H F]? (b) Draw a Venn Diagram that clearly shows all the relevant events and their probabilities. 2. (20 points) A bag contains 10 balls, each of a different color. We randomly draw three balls from
the bag. (a) What is the the number of different color—combinations? (b) One of the balls is blue. How many colorcombinations are there that include the blue ball? 3. (20 points) Two kids sell lottery tickets in your neighborhood and you buy one of their tickets.
Each ticket has two letters on it, you win a prize if your lottery ticket has at least one letter in
common with the code that is drawn [the order is important, for example, AB does not have a
letter in common with BC]. Assuming that all letter—combinations are equally likely, What is the chance that you win a prize? 4. (20 points) How many words can one make with the letters of the word ”avocado”? [Note that
the words do not have to be actual English words] 5. (20 points) After graduating from the University of Wisonsin, Elianna applies to several different
companies. She applies to two companies in Wisconsin, each with two branches, and three
companies in Illinois, two with two branches and one with three branches. (a) Draw a tree that clearly shows both states, the companies and their branches (b) Suppose for the sake of argument that Elianna gets to pick one of these branches and each
branch is equally likely, what would be the chance that she picks a job in Wisconsin? ...
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 Fall '08
 WAINGER
 Math, actual English words

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