Question 1206335
the following table applies:
<pre> 
                         P            N
D                        .07          .03
DC                       .02          .88
</pre>


P means test is positive
N means test is negative
D means disease is present
DC means disease is not present


(a)
Find the following probabilities from the table. (Round your answers to two decimal places.)


P(D)= .07 + .03 = .1
P(DC)= .02 + .88 = .9
P(N|DC)= .88
P(N|D)= .03


(b)
Use Bayes' Rule and the results of part (a) to find P(D|N).
(Round your answer to three decimal places.)


P(D|N) = p(N|D) * p(D) / p(N) = .03 * .1 / .9 = .0033333333 = .003.


(c)
Use the definition of conditional probability to find P(D|N).
(Your answer should be the same as the answer to part (b). Round your answer to three decimal places.)


P(D|N) = = p(D intersect N) / p(N)


from p(N|D), we can solve for p(D intersect N) as follows:
p(N|D) = p(N intersect D) / p(D) becomes .03 = p(N intersect D) / .1
solve for p(N intersect D) to get p(N intersect D) = .03 * .1 = .003.


p(N intersect D) is the same as p(D intersect N) = .003.
p(D|N) = p(D intersect N) / p(N) = .003 / .9 = .0033333333 = .003.


answer in part b and part c are the same, as they should be.


(d)
Find the probability of a false positive, that the test is positive, given that the person is disease-free. (Round your answer to three decimal places.)


probability of a false positive is p(P | DC).
that's the probability you will test positive given that you don't have the disease.
from the table, p(P | DC)) = .02.


(e)
Find the probability of a false negative, that the test is negative, given that the person has the disease.


probability of a false negative is p(N | D).
that's the probability you will test negative given that you have the disease.
from the table, p(N | D) = .03.