assignment2sol

assignment2sol - ELEN 303: Assignment 2 Instructor: Email:...

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ELEN 303: Assignment 2 Instructor: Dr. Jean-Fran¸ cois Chamberland Email: [email protected] (Subject ECEN 303) Ofce: Room 244F WERC Ofce Hours: Tue 2:30 - 3:45 p.m. Problems: 1. Suppose that there are n students in a room, all born in 1985 (a non-leap year). What is the probability that no two o± them celebrate their birthday on the same day o± the year? How large does n need to be so that this probability becomes less than 0.5? Every student in the room celebrates his or her birthday on one o± the 365 days in a year. There±ore there is a total o± (365) n possible outcomes. Assuming that each o± these outcome is equally likely, we can compute the desired probability as 365 · 364 ··· (365 n + 1) 365 n = 365! (365 n )!365 n . Furthermore, when n 23, the probability that no two students celebrate their birthday on the same day is less than 0.5. 2. (FCP: 2.1) A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists o± taking 1 marble ±rom the box, then replacing it in the box and drawing a second marble ±rom the box. Describe the sample space. Repeat when the second marble is drawn without ²rst replacing the ²rst marble. In the ²rst case, the sample space is a ²nite set that contains 9 outcomes. These outcomes can be represented as Ω = { ( r, r ) , ( r, g ) , ( r, b ) , ( g, r ) , ( g, g ) , ( g, b ) , ( b, r ) , ( b, g ) , ( b, b ) } ; the pair ( i, j ) represents a drawing where the color o± the ²rst marble is i , and the color o± the second marble is j . In the second experiment described above, the sample space has 6 outcomes. Using the same labeling scheme as above, these elements are Ω =
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This note was uploaded on 09/07/2008 for the course ECEN 303 taught by Professor Chamberlain during the Fall '07 term at Texas A&M.

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assignment2sol - ELEN 303: Assignment 2 Instructor: Email:...

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