## Relative Frequency Approximation versus Classical Approach to Probability

I have two examples in the textbook that offer explanations of Relative Frequency Approximation and the Classical Approach to Probability.

The first one (Relative Frequency Approximation) states, "A recent Harris Interactive survey of 1010 adults in the United States showed that 202 of them smoke. Find the probability that a randomly selected adult in the United States is a smoker." It goes on to show how to calculate the result of 0.200 and add that "...the classical approach cannot be used since the two outcomes (smoker, non-smoker) are not equally likely."

I think I understand this. The survey shows that about 20% of the population smokes so a random pick wouldn't be 50-50. Is this correct? That's question #1.

It then gives the following table in Example 2 as an example of the Classical Approach:

 Positive Test Result (Drug Use Is Indicated) Negative Test Result (Drug Use Is Not Indicated) Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject is Not a Drug User 90 (False Positive) 860 (True Negative)

It then says, "Assuming that one of the 1000 subjects is randomly selected, find the probability that the selected subject got a positive test result."

It calculates that 134 had positive test results and the probability is 0.134, saying, "the subject is randomly selected, each test result is equally likely, so we can apply the classical approach."

I don't understand why smoker/non-smoker is more unlikely than positive/negative on drug use. That's question #2.

Second, why is each outcome in Example 2 equally likely? The numbers aren't equal and I would (subjectively) expect the results to come out as calculated. I understand examples that show a die roll as having equally probable outcomes but this example eludes me. That's question #3.

Your help, as always, would be greatly appreciated.