Question

A medical test is available to determine whether the patient has a certain disease. To determine the accuracy of the test ,a total of 10,000 people ok tested .only hundred of the people have the disease ,while the other 10,000 are disease-free .Of the disease free people 9800 get the negative results and 200 candidates a positive results .The 100 people with the disease all get the positive results
find the probability that this gives the correct result for a person who does not have the disease​

Answer 1

Answer:

Step-by-step explanation:

Problems like this are complex and the guide to solve them is to always think of all pairs of possibilities; These are 4 now, namely (infected, positive result), (infected, negative result), (not infected, positive result), (not infected, negative result).

If your test shows positive, then either you are infected and the test is correct or you are not and the test is incorrect. The chance for the first event is 10%*95% by the multiplicative law of probabilities, or 0.095. The chance for the second one (to test positively while not infected) is: (1-0.97)* 0.90=0.027

This is the probability that a person is not infected, times the probability that the test indicates that he is infected. So, the total chance of these two scenarios is 0.027+0.095=0.122. The chance that a person with a positive result is actually positive is thus 0.095/0.122=77.9%. Hence, far from sure.

Similarly as above, the false positive is the complimentary probability. The probability across the population that you test positive while not having the disease is 0.027. Thus, the probability is 0.027/0.122=22.1%. This can be also calculated by 100%-77.9%=22,1%, so this serves as a test of our correctness.