Problem Set Week 03

### Second Class

Q102. Kids these days! Of those who get into trouble, it turns out, about 30% are "real trouble-makers" who need some help. The other 70% are normal adolescents who will age out of their trouble-making under normal care. A social worker friend introduces you to a test that you can give to kids who are referred to you to determine which category they are in. Research has suggested the test is 75% accurate. Use tree flipping to describe what to make of the test's results.

Q103. Suppose we are running a program to which we want to accept only individuals in the top 25% of the population (on some measurable trait). Unfortunately, our test for measuring the trait is only 80% accurate. Draw event tree and flip to show what kind of faith we can have in the test results. Which test result appears more worthy of taking at face value? Which group would you be inclined to develop a second test for?

Q104. House gets another case. There's this funny rash. We won't say where it appears, but it's a funny rash. In 1% of the cases, it means something really, really bad — anxoreisis. Fortunately, there's a test. Unfortunately, it's not a perfect test. Fortunately, it's a pretty good test. Unfortunately, it is wrong 2% of the time. Work it out.

Q105. Following on problem 104, suppose the test is not painless or without its own risks. Suppose the "cost" of the test is 5. And suppose the treatment is also not so nice and the cost of the treatment is 15. But if you have the disease and you are not treated, the results are nasty : 50. Do we have enough information to recommend a course of action? What should we do?

Q106. She may love you or she may not. It turns out there is a 40% chance she does. You decide to use the buttercup test to find out (hold a buttercup under chin and see if it reflects yellow). The test is 90% accurate. Draw tree and flip to determine what conclusions we can draw from positive and negative buttercup test results.

[#InClass]]

### In Class/Lab

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