Question

I am having trouble with knowing where to start logically with this type of problem and...

I am having trouble with knowing where to start logically with this type of problem and wondering if someone could explain in some detail on how to apprach this.

Question

Suppose it is known that 1% of the population have a certain kind of cancer. It is
also known that a test for this kind of cancer is positive in 99% of the people who
have it but is also positive in 2% of the people who do not have it. What is the
probability that a person who tests positive has cancer of this type?

Math   Statistics-And-Probability   
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Answer #1

Solution: Let's suppose the population is . From the given information, 1% of the population have a certain kind of cancer. Therefore, we have 100 people with a certain kind of cancer and 9900 people without a certain kind of cancer. It is also known that a test for this kind of cancer is positive in 99% of the people who have it, therefore there are 99 people who have cancer of this kind will test positive. Also we know that 2% of the people who do not have cancer tests positive, that is there are 198 people tests positive who do not have cancer. This information can be put in a tabular form as below:

Therefore, the probability that a person who tests positive has cancer of this type is:

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