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**Unformatted text preview: **EEE 350, Fall 2009 Homework #2 Due Tuesday, 09/15/2009
Problem 1. 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 were rolled. (b) Given that the roll resulted in a sum of 4 or less, find the conditional probability that doubles were rolled. (c) Find the probability that at least one die is a 6. (d) Given that the two dice land on different numbers, find the conditional probability that at least one die is a 6. Problem 2. The disk containing the only copy of your thesis just got corrupted, and the disk got mixed up with three other corrupted disks that were lying around. It is equally likely that any of the four disks holds the corrupted remains of your thesis. Your computer expert friend offers to have a look, and you know from past experience that his probability of finding your thesis from any disc is 0.4 (assuming the thesis is there). Given that he searches on disk 1 but cannot find your thesis, what is the probability that your thesis is on disk i, for i = 1, 2, 3, 4? Problem 3. A new test has been developed to determine whether a given student is overstressed. This test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. It is known that 99.5% of all students are overstressed. Given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed? Problem 4. A magnetic tape storing information in binary form has been corrupted, so it can only be read with bit errors. The probability that you correctly detect a 0 is 0.9, while the probability that you correctly detect a 1 is 0.85. Each digit is a 1 or a 0 with equal probability. Given that you read a 1, what is the probability that this is a correct reading?
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