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Unformatted text preview: STAT/MA 416 August 24, 2011 Problem Set 2 Name: 1. Choosing a page at random. A student buys a brand new calculus textbook that has 1000 pages, numbered from 1 to 1000, of course. She randomly opens the book to a page and starts to read! Assume that any of the 1000 pages are equally likely to be chosen. Find the probability that the page number she chooses contains at least one “5” as a digit. (For instance, each page in the range 500 to 599 contains a “5”, of course, at the start. Also, page 605 has a “5”, and page 257 contains a “5”, and page 055 contains a “5”, etc.) Hint: Use inclusion-exclusion. 1 2. Socks. A matching pair of blue socks, a matching pair of red socks, and one lone white right-footed sock are in a drawer. The socks are pulled out of the drawer, one at a time. (a.) Suppose that a person is looking for the white sock. He repeatedly does the following: He pulls out a sock, checks the color, and if it is white, he stops. If it is not white, then he replaces the sock in the drawer and starts to check again, i.e., he reaches blindly into thereplaces the sock in the drawer and starts to check again, i....
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- Fall '08
- Probability, Probability theory, white sock