4. In July of 2011 the state of Florida started testing all welfare recipients f

Question

4. In July of 2011 the state of Florida started testing all welfare recipients for the use of illegal drugs. Statistics suggest that 8 percent of adult Floridians use illegal drugs; let us assume that this is true for welfare recipients as well. Imagine that the drug test is 92 percent accurate, meaning that it gives the correct response in 92 out of 100 cases. (a) What is the probability that a randomly selected welfare recipient in Florida uses (b) What is the probability that a randomly selected welfare recipient in Florida does (c) What is the probability that a randomly selected welfare recipient in Florida has (d) Given that a randomly selected welfare recipient in Florida has a positive test, illegal drugs and has a positive test? not use illegal drugs but nevertheless has a positive test? a positive test? what is the probability that they use illegal drugs?

Explanation / Answer

Here we are given that: P( illegal drugs ) = 0.08, therefore P( no drugs ) = 1 - 0.08 = 0.92

Also, we are given that it gives 92% correct response. Therefore, we get:

P( positive | illegal drugs ) = P( negative | no drugs ) = 0.92

a) Now the probability that a randomly selected welfare uses illegal drugs and has a positive test is computed as:

P( illegal drugs )P(positive | illegal drugs ) = 0.92*0.08 = 0.0736

Therefore 0.0736 is the required probability here.

b) Now the probability that a randomly selected do not use illegal drugs but still have a positive test is computed as:

P( no drugs , positive ) = 0.92*(1 - 0.08) = 0.0736

Therefore 0.0736 is the required probability here.

c) Now probability that a randomly selected person has a positive test is computed as:

= P( no drugs , positive ) + P( illegal drugs , positive )

= 0.0736 + 0.0736

= 0.1472

Therefore 0.1472 is the required probability here.

d) Given that there is positive test, probability that they use illegal drugs is computed as:

= P( illegal drugs , positive ) / P ( positive )

= 0.0736 / 0.1472

= 0.5

Therefore 0.5 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.