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3solution - ECEN 303: Assignment 3 Problems: 1. Fifty-two...

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Unformatted text preview: ECEN 303: Assignment 3 Problems: 1. Fifty-two 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 6-sided 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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3solution - ECEN 303: Assignment 3 Problems: 1. Fifty-two...

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