Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » General Math Questions


 Page 1 of 1 [ 2 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

5% of the people of your age/heredity..

Author Message
gettoalok
 Post subject: 5% of the people of your age/heredity..
 Post Posted: Tue Mar 09, 2010 7:23 pm 
Offline
Students


Posts: 10
5% of the people of your age/heredity suffer from TB. A blood test was developed that correctly gives a positive test result in 80% of people with TB, and gives a false positive in 20% of the cases of people without TB. Suppose you take the test, and it is positive. What is the probability that you actually have TB, given the positive test result?

Does this problem use conditional probability? If so, please let me know how to use it in this problem?

*I have altered the text significantly enough to make it look completely different from the source text as I couldn't determine the author of this problem.
Top 
esledge
 Post subject: Re: 5% of the people of your age/heredity..
 Post Posted: Sun Apr 25, 2010 11:29 pm 
Offline
ManhattanGMAT Staff


Posts: 903
Location: St. Louis, MO
This is an overlapping set problem with two categories (TB Status and Test Result), best solved with a Double Set Matrix.

Use 100 as the total number of people, for ease of calculation. Thus, 5 have TB and 95 don't. Fill in the rest of the chart based on those numbers and the other percents given.

...........TB........no TB.........Total
Pos...(0.8)(5)...(0.2)(95)
Neg...(0.2)(5)...(0.8)(95)
Total.....5...........95.............100

Computing, this becomes

...........TB........no TB....Total
Pos.......4...........19.......23
Neg......1...........76........77
Total.....5...........95......100

So of all the positive test results (23 cases), 4 are True Positives. The probability is 4/23.

_________________
Emily Sledge
Instructor
ManhattanGMAT
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 2 posts ] 





Who is online

Users browsing this forum: No registered users and 2 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: