Can I get some help on letters D, E, and F 1) The county health department just published a report saying that there is 1% chance that the deadlydisease X exists in the population. There is a screening test for X, and you are encouraged to take thescreening test. However, the test is not perfect. (No test is ever perfect).If you are sick, the test is positive in 90% of cases.If you are not sick, the test is positive in 4% of cases.a) Draw a tree diagram for the story above.Tests +ve0.9Sick0.010.1Tests -vePopulationTests +ve)0.990.4.Not Sick0.6Tests -veb) You take a screen test. What is the probability that you have a positive result?0.405c) You take a screen test. What is the probability that you have a negative result?0.595d) Given that you have a negative result. What is the probability that you have the disease?e) Given that you have a positive result. What is the probability that you don't have the disease?f) Which scenario is more awful? d or e? Explain.

Name: Can I get some help on letters D, E, and F 1) The county health depart
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Can I get some help on letters D, E, and F

1) The county health department just published a report saying that there is 1% chance that the deadly
disease X exists in the population. There is a screening test for X, and you are encouraged to take the
screening test. However, the test is not perfect. (No test is ever perfect).
If you are sick, the test is positive in 90% of cases.
If you are not sick, the test is positive in 4% of cases.
a) Draw a tree diagram for the story above.
Tests +ve
0.9
Sick
0.01
0.1
Tests -ve
Population
Tests +ve)
0.99
0.4.
Not Sick
0.6
Tests -ve
b) You take a screen test. What is the probability that you have a positive result?
0.405
c) You take a screen test. What is the probability that you have a negative result?
0.595
d) Given that you have a negative result. What is the probability that you have the disease?
e) Given that you have a positive result. What is the probability that you don't have the disease?
f) Which scenario is more awful? d or e? Explain.

Expert Solution

Step 1

d) Given that the probability of having the disease is 1%=0.01

$We have to find P (have disease | negative result) P (have disease | negative result) = \frac{P (have disease and negative result)}{P (negative result)} = \frac{P (have disease and negative result)}{P (have disease and negative result) + P (do not have disease and negative result)} = \frac{P (have disease) \times P (negative result | have disease)}{P (have disease) \times P (negative result | have disease) + P (do not have disease) \times P (negative result | do not have disease)} = \frac{0.01 (1 - 0.90)}{0.01 (1 - 0.90) + (1 - 0.01) (1 - 0.04)} = 0.00105108261509 Answer (d) : 0.00105108261509$

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