HW 1 Solution

# HW 1 Solution - E 243 2016 Fall HW#1 Solutions Due Sept...

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E 243- 2016 Fall HW #1 Solutions Due: Sept 12 th Total Points -100 2-20. Three events are shown on the Venn diagram in the following figure: (2+2+2+2+2 points) Reproduce the figure and shade the region that corresponds to each of the following events. (a) ?′ (b) (? ∩ ?) ∪ (? ∩ ?′) (c) (? ∩ ?) ∪ ? (d) (? ∪ ?)′ (e) (? ∩ ?)′ ∪ ? Sol: (a) (b) (c)

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(d) (e) 2-28. Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows: (10 points) Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample conforms to specifications. Determine the number of samples in ?′ ∩ ? , ?′ , and ? ∪ ? . Sol: B A = 55 , B =23, B A = 85 2-54. Similar to the hospital schedule in Example 2-11, suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries. (4+4+4 points) (a) How many different sequences are possible? (b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively? (c) How many different schedules begin and end with a knee surgery?
Sol: (a) From the formula for the number of sequences 12! 3!4!5! = 27,720 sequences are possible. (b) Combining all hip surgeries into one single unit, all knee surgeries into one single unit and all shoulder surgeries into one unit, the possible number of sequences of these units = 3! = 6 (c)With two surgeries specified, 10 remain and there are 10!

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