I know this is a big problem but if you can expalin this problem as much you can

Question

I know this is a big problem but if you can expalin this problem as much you can, it will be really appreciated.

C Suppose a diagnostic test for a condition known as Condition X has the following results: test actua Yes20 1 No 80 1899 Here "actual" is whether a person actually has condition X or not, while "test" is the result of the test or 1. What are this test's false positive and false negative rat es? 2. What is the percentage of the sample having condition X? 3. Given that a person tests positive, what is her/his probability of having Condition X? 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 X.

So

P(false positive) = P(+ | No) = 80 / 1979

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

So

P(false negative) = P(- | Yes) = 1 / 21

2)

P(condition X) = 21 /2000 = 0.0105 =1.05%

3)

P(Yes | +) = 20 /100 = 0.20

4)

Conditonal probability shows that out of 100 positive results, 20 have condition X.

test + - Total actual Yes 20 1 21 No 80 1899 1979 Total 100 1900 2000

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