Question

The following table shows one month’s results from a public health clinic’s testing for a new strain of flu during a pandemic that were confirmed the following month. Examine the results and answer the first four questions.

Patients With               Patients Without

                                                            New Flu                     New Flu

Patients Testing Positive             200                            100

Patients Testing Negative             50                             700

An anxious patient arrives at the clinic wanting to get tested. As the physician, you try to assuage their concerns and tell them that the test does a good job in identifying someone infected. “How well?” asks the distraught patient. What percentage chance does the test have in correctly identifying the patient as being truly sick or not sick?

Chance for test identifying someone truly sick:

Chance for test identifying someone truly well:

Answer 1

Answer :

As we need to identify that there are 1050 analysis to be taken care:

so out of 1050, 200 test seems positive and they have actually with flue so probabilty = 200/1050 = 0.19047

so out of 1050, 50 test seems negative and they have actually with flue so probabilty = 50/1050 = 0.04762

so out of 1050, 200 test seems positive and they have actually without flue so probabilty = 100/1050 = 0.09524

so out of 1050, 200 test seems negative and they have actually without flue so probabilty = 300/1050 = 0.66667

If we make the table:

Test/actual	With Flue	Without Flue
Positive	0.19047	0.095238
Negative	0.04762	0.66667

i)

so out of 250 really sick person 200 test can be identified by the test

so total probability = 200/250 =0.8

In bayes term P(positive| person is with new flue) = P(positive test ∩ person with flue) / person having flue

= 0.19047 /(0.19047+0.04762)

= 0.799

So total 0.8 probability that if the person having new flue and test shows the positive result

II)

so out of 800 person having no flue 700 got negative by thest

so total probability = 700/800 = 0.875

In bayes term P(negative test| person is without new flue) = P(negative test ∩ person without flue) / person having no flue

= 0.66667 /(0.66667+0.095238)

= 0.875

So total 0.875 probability that if the person having no new flue and test shows the negative result