A person has a test for a nasty disease. Use the random variable x to describe the person’s health condition:
x = 1 : the person has the disease,
x = 0 : the person does not have the disease.
Similarly, we use the random variable y to describe the test result. The result of the test is either “positive” ( y = 1) or “negative” ( y = 0). The test is 95% reliable, i.e., in 95% of cases of people who really have the disease, a positive result is returned, and in 95% of cases of people who do not have the disease, a negative result is obtained. A final piece of information is that 1% of those of the person’s age and background have the disease.
The person has the test, and the result is positive. What is the probability that the person has the disease? Hint Use the conditional probability.
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