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Unformatted text preview: 310-1 Fall 2010Final ExamDecember 10, 2010Directions:Write your name and your professors name on the cover of your exam booklet. Calculators,books, notes or any other study aids may NOT be used. Show all work and clearly mark your finalanswers.Answers given as formulas in terms of combinatorial notation will be accepted. Answers that can beeasily simplified should be simplified. Express all normal probabilities in terms of the distributionfunction of the standard normal, i.e. (x) =12Rx-e-12u2du.1. (25 points) A computer password of 8 characters is made of 26 letters, 10 digits, and 20 specialsymbols on the keyboard of a computer. In how many ways can you form these passwords if(a) there is no restriction;(b) there is no digit and all the rest are different;(c) there are exactly three special symbols;(d) the first character is a letter, there are exactly two different special symbols and only onedigit.2. (20 points) There are 3 coins in a box. One is a two-headed coin; another is a fair coin; and thethird is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins isselected at random and flipped, it shows heads. What is the probability that it was the two-headedselected at random and flipped, it shows heads....
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This note was uploaded on 01/03/2012 for the course MATH 310-1 taught by Professor Sarver during the Spring '11 term at Northwestern.
- Spring '11