A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.06. It is estimated that 6% of the population who take this test have the disease. (Round your answers to three decimal places.)
(a) If the test administered to an individual is positive, what is the probability that the person actually has the disease?

(b) If an individual

Question

A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.06. It is estimated that 6% of the population who take this test have the disease. (Round your answers to three decimal places.)
(a) If the test administered to an individual is positive, what is the probability that the person actually has the disease?


(b) If an individual

anonymous · Answer

(b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)

anonymous · Answer

bayes formula for this one, but if it is confusing use actual numbers
choose big ones, like $1,000,000$

anonymous · Answer

actually maybe you don't need a number that big, because $6\%$ of the population has it
a rather common disease i guess
want to try it with $10,000$ ?

anonymous · Answer

okay yes

anonymous · Answer

ok lets make our sample size $10,000$ that should be big enough
you are told $6\%$ of the population has the disease
what is $6\%$ of $10,000$ ?

anonymous · Answer

600

anonymous · Answer

ok good, so we know $600$ people have the disease, and the rest $9,400$ so not have it

anonymous · Answer

of the $600$ who have it, the test detects it in $95\%$ of them, and $.95\times 600=570$ so $570$ who have the disease test positive

anonymous · Answer

$6\%$ of the people who do not have the disease will get a false positive, and $.06\times 9400=564$

anonymous · Answer

the total number of positive tests is therefore $570+564=1134$ and of those $1134$ you know $570$ have the disease, so the probability that the person who tests positive actually has the disease is 
$$\frac{570}{1134}$$

anonymous · Answer

we can redo the problem without the $10,000$ if you like
and just work with the decimals, but usually a nice large sample size makes the idea a lot easier to understand

anonymous · Answer

how do I get B after I get A??? I got 0.503 for A

anonymous · Answer

not sure how to set up B