ONLY ANSWER QUESTION 4.b 4. (4 pts each) Sheryl works in a law office as a paral
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ONLY ANSWER QUESTION 4.b
4. (4 pts each) Sheryl works in a law office as a paralegal, where she quickly scans hundreds of documents looking for smoking guns, a significant piece of evidence in support of their side Occasionally she will find an oh s***, a significant piece of evidence against their side in a case. If she find either a smoking gun or an oh s***, she immediately contacts the head lawyer in the case to discuss what she found. We will assume finding a significant piece of evidence from document to document are independent events. (a) For a particular case, suppose Sheryl's chances of finding a smoking gun is .00045, and her chances of finding an oh s*** is .00032, both of which are really small numbers. Find the expected number of documents Sheryl would need to scan before needing to contact the head lawyer (b) A particular case has 40,000 documents (this would be a typical size for the type of cases Sheryl assists with). Each document has a chance p = .00004 of containing a smoking gun. Estimate the chances of having 3 or more smoking g uns in the case (c) Suppose the chances of finding a smoking gun is .0004 and the chances of finding a oh s*** is .0006. Calculate the probability that Sheryl finds two oh s***s before the first smoking gun. Here you may assume the number of documents are endless, as they often seem to be in law cases (d) A head lawyer has promised Sheryl a gift certificate to Highlands Grill if she can find three or more smoking guns for a particular case. Assuming that the number of documents are endless, and the chances of finding a smoking gun is .00004, what is the expected number of documents Sheryl needs to scan for her math professor husband to enjoy a night out at Highlands Grill? (e) Suppose the time it takes Sheryl to scan documents are independent identically dis- tributed random variables. She clearly reads many, many, many documents for each case. Explain how you would model the average amount of time it takes Sheryl to scan a case. How do you justify your model?Explanation / Answer
(b) Here Pr(containing a smoking gun) = 0.00004
Number of documents = 40000
Pr(X >=3 ) = 1 - [Pr(X = 0) + Pr(X = 1) + Pr(X =2)]
=1 - [ BIN (X = 0; 40000 ; 0.00004) + BIN (X = 1; 40000 ; 0.00004) + BIN (X = 2; 40000 ; 0.00004)]
= 1 - [ 0.2019 + 0.3230 + 0.2584]
= 1- 0.7833
= 0.2167
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