probability (expected value) help pls...? - XP Math - Forums

 XP Math - Forums probability (expected value) help pls...?

 08-05-2007 #1 cute_gurl Guest   Posts: n/a probability (expected value) help pls...? R={test result is positive}, D={person has the disease}.Assume that for a randomly selected person, P(D) = 0.02, P(R|D) = 1, P(R| not D) = 0.05, so that the inexpensive test only gives false positive, and not false negative, results.Suppose that this inexpensive test costs \$10. If a person tests positive then they are also given a more expensive test, costing \$100, which correctly identifies all persons with the disease . What is the expected cost per person if a population is tested for the disease using the inexpensive test followed, if necessary, by expensive test?
 08-05-2007 #2 TheSpoon Guest   Posts: n/a It would be helpful to find out the probability of administering the expensive test to any person. Call this P(E).P(E) = P(E|D)P(D) + P(E|~D)P(~D) as you can check.(~ means not).What's P(E|D)? This is P(R|D) since if they have the disease then the result of the first test is positive and so they are given the expensive test.What's P(E|~D)? This is P(R|~D) since if they don't have the disease, the probability of getting the expensive test is the probability that the first test result is positive.So we can calculate P(E):P(E) = P(E|D)P(D) + P(E|~D)P(~D)= 1*0.02 + 0.05*0.98= 0.0686.Using this we can compute the expected cost of testing a person.It costs at least \$10 to test each person, and with probability P(E) we'll have to spend another \$100. So the expected cost is 10 + P(E)*100 = 16.86.

 Thread Tools Display Modes Hybrid Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Welcome     XP Math News     Off-Topic Discussion Mathematics     XP Math Games Worksheets     Homework Help     Problems Library     Math Challenges

All times are GMT -4. The time now is 07:38 PM.

 Contact Us - XP Math - Forums - Archive - Privacy Statement - Top