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problemset03 - STAT/MA 416 Problem Set 3 Name 1 Choosing a...

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STAT/MA 416 August 26, 2011 Problem Set 3 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. Let A be the event that the first digit on the chosen page is a “5” (for example, the page could be 572). Let B be the event that the second and third digits on the chosen pages are both “5” (for example, the page could be 455). Are A and B independent? Why? Justify your answer. 1
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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. 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 the drawer of 5 socks. He continues to do this over and over until he finds the white sock, and
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