AMS 311 Hw 1 - AMS 311(Fall 2011 Joe Mitchell PROBABILITY...

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AMS 311 (Fall, 2011) Joe Mitchell PROBABILITY THEORY Homework Set # 1 Due at the beginning of class on Thursday, September 8, 2011. Reminder: Show your reasoning! Read: Ross, sections 1.1-1.4 of Chapter 1, and sections 2.1-2.5 of Chapter 2 . SPECIFICS OF READING ASSIGNMENT: Examples to read carefully: Chapter 1: 2a–2e; 3a–3f; 4a–4e Chapter 2: 3a, 3b, 4a, 5a–5j, 5l (1). (13 points) A system is comprised of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ), where x i is equal to 1 if component i is working and is equal to 0 if component i is failed. (a). How many outcomes are in the sample space of this experiment? (b). Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are working, or if components 1, 3, and 5 are all working. Let W be the event that the system will work. Specify all of the outcomes in W . (c). Let A be the event that components 4 and 5 are both failed. How many outcomes are
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