. Suppose 2% of people have Syndrome X. We have a Syndrome X detecting test which...

Free

60.1K

Verified Solution

Question

Statistics

. Suppose 2% of people have Syndrome X. We have a Syndrome Xdetecting test which gives which gives a positive result for 90% ofpeople who do have the syndrome, but also gives a positive resultfor 10% of people who donâ€™t actually have the syndrome. A patientcomes in and gets a positive result. What are the chances they haveSyndrome X? For full credit, you must show your work.

Answer & Explanation Solved by verified expert

3.9 Ratings (403 Votes)

P(people have Syndrome X) = 0.02

P(positive result | have Syndrome X) = 0.9

P(positive result | don't have Syndrome X) = 0.1

P(positive result) = P(positive result | have Syndrome X) * P(have Syndrome X) + P(positive result | don't have Syndrome X) * P(don't have Syndrome X)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.9 * 0.02 + 0.1 * (1 - 0.02)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.116

P(have Syndrome X | positive result) = P(positive result | have Syndrome X) * P(have Syndrome X) / P(positive result)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.9 * 0.02 / 0.116

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.1552 ( ans)

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member