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Are you ill? (Posted on 2005-01-03) Difficulty: 3 of 5
Suppose an illness that can affect 1% of the people. Also assume that there is a test for that illness, that gives the correct result 99% of the times.

If you take that test, and receive a POSITIVE result, should you worry much?

If you take it again, and once more get a POSITIVE, should you worry then?

How many consecutive POSITIVEs would you have to get in order to be sure that the chances of a wrong diagnostic are 1 in a million?

  Submitted by e.g.    
Rating: 3.7500 (4 votes)
Solution: (Hide)
For the first test, 1% of the 99% of sane people get a (wrong) POSITIVE, as do 99% of the 1% ill people, so the chances of the result being correct are 50%-50%.

After the second test, odds change to 99%-1%, so you are wrong 1 out of 100 times; after the third, 99.9898798%-0.010202%, so you are wrong 1 out of 9802 times, and after the fourth, you'd be wrong 1 out of 970,300 times, close enough to 1 million.

By the way, three more tests would make your chances of being wrong 1 in 96 million, 1 in 9.5 billion, and 1 in 941 billion.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Correct Solution (for real)Marc2005-10-19 23:10:44
SolutionCorrect Solution.A2005-03-06 06:30:10
Implications to our justice systemajosin2005-02-28 14:46:13
re: Combined probabilitiesKyle2005-01-07 15:37:44
re: Combined probabilitiesDJ2005-01-07 12:51:58
Combined probabilitiesFrançois2005-01-06 17:16:22
perplexus in the newsPenny2005-01-04 02:34:16
re(5): solutionLarry2005-01-03 22:39:13
re(4): solutionPenny2005-01-03 21:23:49
re(3): solutionKyle2005-01-03 21:15:43
re(2): solutionLarry2005-01-03 20:37:44
re: This is a lousy example, but...Eric2005-01-03 20:25:07
This is a lousy example, but...Penny2005-01-03 20:08:16
re(2): solutionEric2005-01-03 20:05:06
re: solutionPenny2005-01-03 18:26:15
solutionCharlie2005-01-03 18:01:27
QuestionIs your terminology correct ?Penny2005-01-03 17:40:33
SolutionMeaning?Angela2005-01-03 17:28:48
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