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Unformatted text preview: ECEN 303: Assignment 3 Problems: 1. Fiftytwo percent of the students at a certain college are females. Five percent of the students in this college are majoring in computer science. Two percent of the students are women ma joring in computer science. If a student is selected at random, find the conditional probability that (a) this student is female, given that the student is majoring in computer science; (b) this student is majoring in computer science, given that the student is female. Let F represent the set of female students, and let CS be the group of students mojoring in comptuer science. From the problem statement, we have Pr( F ) = 0 . 52 , Pr( CS ) = 0 . 05, and Pr( F CS ) = 0 . 02. The conditional probability that a student selected at random is female, given that the student is majoring in computer science, is equal to Pr( F  CS ) = Pr( F CS ) Pr( CS ) = 2 5 . Similarly, the conditional probability that a student selected at random is majoring in com puter science, given that the student is female, can be computed as Pr( CS  F ) = Pr( CS F ) Pr( F ) = 2 52 = 1 26 . 2. We roll two fair 6sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. (a) Find the probability that doubles are rolled. Each possible outcome has probability 1 36 . There are 6 possible outcomes that are doubles, so the probability of doubles is 6 36 = 1 6 . (b) Given that the roll results in a sum of 4 or less, find the conditional probability that doubles are rolled. The conditioning event (sum is 4 or less) consists of the 6 outcomes { (1 , 1) , (1 , 2) , (1 , 3) , (2 , 1) , (2 , 2) , (3 , 1) } , 2 of which are doubles, so the conditional probability of doubles is 2 6 = 1 3 . (c) find the probability that at least one die roll is a 6. There are 11 possible outcomes with at least one 6, namely, (6 , 6), (6 ,i ), and ( i, 6), for i = 1 , 2 ,..., 5. Thus, the probability that at least one die is a 6 is 11 36 ....
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 Fall '07
 Chamberlain
 Computer Science

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