Hi if possible can you also explain how you got it as much as you can, I would r

Question

Hi if possible can you also explain how you got it as much as you can, I would really appreciate it. Sorry this question is long but if you can atleast answer my main question which is the 4th one it would be great

C Suppose a diagnostic test for a certain condition has the following results: test actual Ye 40 1 No 400 8559 1. What are the test's false positive and false negative rates? 2. What is the percentage of the sample having the concition? 3. A patient tests positive, is aware of the test's very low false positive rate, and asis "Doc, wlat are my chances?" What do you tell the patient? What is ha/his probabiliy stally having the condition? If they don't believe you, how do ycu explain? 4. Can you explain using the idea of conditional probability?

Explanation / Answer

Following table shows the row total and column total:

(a)

False positive means test gives positive results given that person do not have condition.

So

P(false positive) = P(+ | No) = 400 / 8959 = 0.0446

False negative means test gives negative results given that person have condition .

So

P(false negative) = P(- | Yes) = 1 / 41 = 0.0244

2)

P(condition X) = 41 /9000 = 0.0046 =0.46%

3)

P(Yes | +) = 40 / 440 =0.0909 =9.09%

That is if a person test positive then there is only 9.09% chances that person has condition.

Dr shoud suggest the patient for retest becuse chances of havig disease is low if he/she test positive.

4)

Conditonal probability shows that out of 440 positive results, only 40 have condition. That is only 9.09% of positive test results are correct.

test + - Total actual Yes 40 1 41 No 400 8559 8959 Total 440 8560 9000

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