(10 points) Suppose that only 2% of individuals undergoing a particular medical

Question

(10 points) Suppose that only 2% of individuals undergoing a particular medical test have the disease that the test is indending to identify. If an individual has the disease the probability that the test will correctly identify the presence of the disease is 0.99. If an individual does not have the disease the probability that 7 the test falsely gives a positive result is 0.10. (a) (4 points) Create a hypothetical one hundred thousand table illustrating this situation, where the row categories are disease (yes, no) and the column categories ar test results (positive, negative). Discase No discase Test 444 29 , 8o (b) (4 points) Draw a tree diagram for this situation. 0o,00 total r(yes d.seasc 4cS+)®.002Lqq ve s no 99g disease (c) (1 point) Using the table from (a) or the tree diagram from (b), find the proportion of people who will test positive for the disease. lo, i7S/1oo,ooo-o.10/78 10.18% or (d) (1 point) Find the probability that you actually have the disease given that your test results are positive. (0.440 .co3)(0.10)(0.99) ..), "10.0 1008. ..,., ,

Explanation / Answer

There is one small mistake in the solution b part

Instead of 0.002 we need to use 0.02 as it is 2% and not 0.2%.

Now the entire tree changes

P(yes disease and positive test ) = 0.02*0.99 = 0.0198

P(yes disease and negative test ) = 0.02*0.01 = 0.0002

P(No disease and positive test ) = 0.98*0.1 = 0.098

P(No disease and negative test ) = 0.98*0.9 = 0.882

c)0.0198+0.098 = 0.1178

d)0.0198/0.1178 = 0.168

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