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Unformatted text preview: EE 131A Midterm Practice Problem Set Instructor: Vwani Roychowdhury Problems 1 through 4 comprised the midterm exam for Fall 2004. 1. (30 pts) A box contains 3 distinct dice. Die #1 is a fair die. Die #2 lands on 1 with probability 1/4, on 6 with probability 1/4 and has probability 1/8 of landing on each of 2, 3, 4, and 5. Die #3 lands on 1 with probability 1/3, on 6 with probability 1/3, and has probability 1/12 of landing on each of 2, 3, 4, and 5. (a) ( 10 pts ) If die #2 is rolled twice, then find the probability that the sum of the two outcomes is 8. (b) Next, one of the three dice is chosen at random and rolled twice. i. ( 10 pts ) Find the probability that the sum of the two numbers rolled is 8. ii. ( 10 pts ) Given that the numbers rolled are both 6, what is the probability that the fair die (i.e., die #1) has been chosen? 2. (25 pts) The color of a persons eye is determined by a single pair of genes. If they are both blue-eyed genes, then the person will have blue eyes; if they are both brown-eyed genes then the person will have brown eyes; and if one of them is a blue-eyed gene and the other a brown-eyed gene, then the person will have brown eyes. (Because of the latter fact, we say that the brown-eyed gene is dominant over the blue-eyed one.) A newborn child independently receives one eye gene from each of its parents and the gene...
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