A doctor gives a patient a test for a particular virus. Before the results of th

Question

A doctor gives a patient a test for a particular virus. Before the results of the test, it is believed that .15% of the population has this virus. Based on experience, the doctor knows that, in 98% of the cases in which the virus is present, the test is positive; and in 93% of the cases in which the virus is not present, the test is negative. Use a hypothetical 100,000 table to find the following.

A). A patient was given the test and it came back positive. What is the chance that the virus is present? Please set up hypothetical the table of 100,000. (thank you)

B). If the person was tested negative, what is the chance the patient is healthy (i.e., the virus is not present)?

C). Without doing any calculation, would you expect your answer in part (a) to increase or decrease if it is believed that 1 in every 1250 people has the virus? Explain your answer briefly.

Explanation / Answer

(A) Here the hypothetical 100,000 table

Where The diseased people who has the viruses are = 100,000 * 0.15/100 = 150

Tested positive out of 150 = 0.98 * 100 = 147

Test negative when negative = 0.93 * (100000 - 150) = 92861

(A) The tested results positive,

Pr(Virus is present l tested positive) = 147/7137 = 0.0206

(B) Pr(Patient is healthy l Tested negative) = 92861/92864 = 0.99997

(C) Now we are not doing any calculation but we know that

Pr(Diease) = 1/1250 which is lower than 0.15% so we can say that our answer to question (a) will decrease as probability to find a diseased person is now more reduced so the part(a) problem whic entails that if test positve, the patient have the disease will further reduce.

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