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Answer:
There is approximately 17% chance of a person not having a disease if he or she has tested positive.
Step-by-step explanation:
Denote the events as follows:
<em>D</em> = a person has contracted the disease.
+ = a person tests positive
- = a person tests negative
The information provided is:
Compute the missing probabilities as follows:
The Bayes' theorem states that the conditional probability of an event, say <em>A</em> provided that another event <em>B</em> has already occurred is:
Compute the probability that a random selected person does not have the infection if he or she has tested positive as follows:
So, there is approximately 17% chance of a person not having a disease if he or she has tested positive.
As the false negative rate of the test is 1%, this probability is not unusual considering the huge number of test done.