04 STAT HWA q probability - Dr. V.R. Bencivenga Economics...

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1 Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #4A: PROBABILITY 1. Hydraulic landing assemblies coming from an aircraft rework facility are inspected for defects. Historical records indicate that 8% have defects in shafts only, 6% have defects in bushings only, and 2% have defects in both. One of the hydraulic assemblies is selected at random. What is the probability the assembly has a. a bushing defect b. a shaft or bushing defect c. exactly one of the two types of defects d. neither type of defect 2. In a game, a player is given three attempts to hit a ball. On each attempt, she either scores a hit (H) or a miss (M). The game requires the player to alternate which hand she uses, i.e., she can make three attempts using RLR or LRL. Her chance of scoring a hit with her right hand is .7 and with her left hand is .3, so she starts with her right hand (RLR). Results of successive attempts are independent. She wins if she scores at least two hits in a row. a. Give the sample space generated by this experiment. What is the probability distribution over the sample space? b. What is the probability she wins the game? 3. Consider an experiment in which five fibers, which have lengths one, two , three, four, and five inches, respectively, are tested to see which breaks first. Suppose that the probability that any given fiber will break first is proportional to the length of that fiber. Give the sample space, and the probability distribution over the sample space. 4. A publisher has six textbooks in physics in its catalog. The publisher is deciding on its advertising strategy regarding these textbooks. Each textbook can be advertised, or not. Think of this decision as a random trial. a. How many distinct outcomes are possible? b. Of these outcomes, in how many are four or more of the physics textbooks advertised? c. A marketing specialist is hired to rank the six texts according to projected sales over the next two years. How many distinct rankings are possible? d. The publisher decides to commission new editions of three of the six physics textbooks, one in each of the next three years. The marketing specialist is asked to choose three texts for new editions, specifying the text to be updated in the first year, the text to be updated in the second year, and the text to be updated in the third year. How many distinct rankings are possible? e. The publisher decides that it will begin an annual mailing to physics professors of an advertising pamphlet that focuses on three of its six physics texts. The company does not want to focus on the same three texts more than once. It does not mind repeating one or two of them, but it does not want all three to be the same as in a previous mailing. How many years can the publisher stick to this policy before it is forced to change it?
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This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas at Austin.

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04 STAT HWA q probability - Dr. V.R. Bencivenga Economics...

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