Question

1. Statistics suggest that some 6% of Florida adults use illegal drugs, assume this is true for welfare recipients too. Imagine the drug test is 92% accurate.
   1. What is the probability that a randomly selected Floridian welfare recipient uses illegal drugs and has a positive test?

2. What is the probability that a randomly selected Floridian welfare recipient does not use illegal drugs but nevertheless has a positive test?

3. What is the probability that a randomly selected Floridian welfare recipient has a positive test?
4. Given that a randomly selected Floridian welfare recipient has a positive test, what is the probability that he or she uses illegal drugs?
5. If a voter favors the drug-testing law because he thinks the answer to d is in the neighborhood of 90%, what fallacy might he be committing?

Answer 1

(a) The probability that a randomly selected Floridan welfare recipient uses illegal drugs and has a positive test = 0.06*0.92 = 0.052

(b) The required probability = 0.94*0.08 = 0.0752

(c) Probability that a randomly selected Floridan welfare recipient has a positive test = 0.052 + 0.0752 = 0.1272

(d) The required probability = 0.052/0.1272 = 0.4088

(e) The fallacy is that he is not considering that there is higher percentage of Floridan welfare recipient who does not uses illegal drugs because of which the required probability is less than that of the accuracy of the test