## anonymous one year ago A new medical screening test is used to detect a rare, non-life-threatening condition. If a person has this condition, the test always detects it. Approximately 0.2% of the population has the condition. Over many trials, the test returns a positive result 6% of the time. Julio takes the test and gets a positive result. To the nearest tenth of a percent, what is the probability that Julio actually has the condition?

1. anonymous

@triciaal

2. triciaal

@marihelenh

3. marihelenh

@triciaal Earlier when I was working on those percent problems, were you there and trying them also? I think I have an idea, but I will need you to check it.

4. triciaal

|dw:1437440977572:dw|

5. marihelenh

That is not what I got. That isn't even how I interpreted the question.

6. triciaal

sorry don't care for stats

7. triciaal

@Nnesha help?

8. triciaal

@jim_thompson5910 stats

9. triciaal

@marihelenh percent ok probability part of stats need to be verified

10. jim_thompson5910

D = person has disease T = test returns positive If a person has this condition, the test always detects it means P(T|D) = 1 Approximately 0.2% of the population has the condition ---> P(D) = 0.002 Over many trials, the test returns a positive result 6% of the time ---> P(T) = 0.06 Use Bayes Theorem to get $\Large P(D|T) = \frac{P(T|D)*P(D)}{P(T)}$ $\Large P(D|T) = \frac{1*0.002}{0.06}$ $\Large P(D|T) \approx 0.0333$ So if the test returns positive, then there is a 3.33% chance (roughly) that he has the condition.

11. anonymous

Thank you all!

12. marihelenh

Aahhh, I would have had it right golly gee! That was what I got but in a much simpler way.