You test positive for a condition and you find out that the test is 90% accurate

Question

You test positive for a condition and you find out that the test is 90% accurate. What is the probability that you have the condition? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(b) You are at the doctor's office and have just tested positive for a disease. The test accurately indicates the disease in 90% of the people who have it, and it accurately indicates no disease in 80% of the people who do not have it. What is the false positive rate (probability of a false positive)? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(c) The base rate of the disease is 1%. In a city of 600000 people, approximately how many people have the disease?Answer (d) Using the information in the previous parts, what is the probability that you have the disease given that the test was positive? Give your answer rounded to four decimal places. You test positive for a condition and you find out that the test is 90% accurate. What is the probability that you have the condition? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(b) You are at the doctor's office and have just tested positive for a disease. The test accurately indicates the disease in 90% of the people who have it, and it accurately indicates no disease in 80% of the people who do not have it. What is the false positive rate (probability of a false positive)? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(c) The base rate of the disease is 1%. In a city of 600000 people, approximately how many people have the disease?Answer (d) Using the information in the previous parts, what is the probability that you have the disease given that the test was positive? Give your answer rounded to four decimal places. You test positive for a condition and you find out that the test is 90% accurate. What is the probability that you have the condition? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(b) You are at the doctor's office and have just tested positive for a disease. The test accurately indicates the disease in 90% of the people who have it, and it accurately indicates no disease in 80% of the people who do not have it. What is the false positive rate (probability of a false positive)? Please select one: 0.9 0.1 0.8 0.2 more information is needed
(c) The base rate of the disease is 1%. In a city of 600000 people, approximately how many people have the disease?Answer (d) Using the information in the previous parts, what is the probability that you have the disease given that the test was positive? Give your answer rounded to four decimal places.

Explanation / Answer

a) Since the test is 90% accurate so every result is 90% probable of having it, that's why given that the result is positive: the probability of having the condition(means positive) = 0.9

b) probability when the result was positive but was false = means that probability when people who do not have the disease but it will show positive = 1- 0.8 = 0.2

since 0.8 is the probability when people had no disease and it showed no disease only.

=> 0.2 is the probability when people had no disease but result shows positive i.e FALSE POSITIVE

Therefore answer = 0.2

c)Since 1% is base rate of disease

=> that out 100 people 1 person had disease, therefore

In a city of 600000 people, the people who have disease = 600000*(1/100)

= 6000 people

d) In both parts a) and b) given that the test is positive, the accuracy when it is positive is 90% so the probability of having a disease when its positive = 0.9

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