::: Questions Assignment Score: 33.3% xCollapse pe Resources Give Up? Feedback R

Question

::: Questions Assignment Score: 33.3% xCollapse pe Resources Give Up? Feedback Resume Question 3 of 3> Attempt 2 1. Question In Progress 3 Attempts 0% 2. Question Correct 1 Attempt Suppose that 0.5% of male professional golfers use steroids, and that Max is a male professional golfer who has been randomly selected to take a drug test. The test he has been asked to take has a false positive rate of 1% and a false negative rate of 10%. Use Bayes' rule to calculate the probability that Max actually uses steroids if he tests positive for steroid use. Give your answer as a decimal precisc to three decimal placcs. 100% 3. Question In Progress 2 Attempts P0.332 0% Assignment Info Tools

Explanation / Answer

Question 1:
Here, we are given that:

P( steroids ) = 0.005

Also, we are given that:

P( positive | no steroids ) = 0.01, therefore P( negative | no steroids ) = 0.99
P( negative | steroids ) = 0.10, therefore P( positive | steroids ) = 0.9

Using law of total addition, we get here:
P( positive ) =  P( positive | steroids )P( steroids ) + P( positive | no steroids ) P( no steroids )
P( positive ) = 0.9*0.005 + 0.01*(1 - 0.005) = 0.01445

Using bayes theorem, we get here:

P( steroids | positive ) = P( positive | steroids )P( steroids ) / P( positive )

P( steroids | positive ) = 0.9*0.005 / 0.01445 = 0.3114

Therefore 0.311 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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