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Unformatted text preview: CS112 - Homework #2 When solving these problems make sure to follow the problem solving steps described in lecture 2, slide #2: 1. Define appropriate notation for components of the problem. 2. Express given information in formal terms using the notation (Sample space, given prob- abilities, etc.) 3. Express what you have to solve for in formal terms using the defined notation. 4. Derive the required result 5. If reasonable, perform sanity checks 1. There are two events A and B , both with nonzero probabilities. If the occurrence of B makes occurrence of A more likely, is it ALWAYS true that the occurrence of A also makes occurrence of B more likely? (hint: B makes occurrence of A more likely can be represented as P ( A | B ) > P ( A ) ) 2. A parking lot consists of a single row containing n parking spaces ( n 2). Mary arrives when all spaces are free. Tom is the next person to arrive. Each person makes an equally likely choice among all available spaces at the time of arrival. (a) Describe the sample space. (b) Obtain P ( A ), the probability the parking spaces selected by Mary and Tom are at most 2 spaces apart(that is, at most 1 empty space between them). 3. A large ISP ran an experiment over 1 year to determine the predominance of spam email on their servers. It turns out that of all the mails they have received, 20% are spam....
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- Spring '08