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 Are you ill? (Posted on 2005-01-03)
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) Marc 2005-10-19 23:10:44 Correct Solution. A 2005-03-06 06:30:10 Implications to our justice system ajosin 2005-02-28 14:46:13 re: Combined probabilities Kyle 2005-01-07 15:37:44 re: Combined probabilities DJ 2005-01-07 12:51:58 Combined probabilities François 2005-01-06 17:16:22 perplexus in the news Penny 2005-01-04 02:34:16 re(5): solution Larry 2005-01-03 22:39:13 re(4): solution Penny 2005-01-03 21:23:49 re(3): solution Kyle 2005-01-03 21:15:43 re(2): solution Larry 2005-01-03 20:37:44 re: This is a lousy example, but... Eric 2005-01-03 20:25:07 This is a lousy example, but... Penny 2005-01-03 20:08:16 re(2): solution Eric 2005-01-03 20:05:06 re: solution Penny 2005-01-03 18:26:15 solution Charlie 2005-01-03 18:01:27 Is your terminology correct ? Penny 2005-01-03 17:40:33 Meaning? Angela 2005-01-03 17:28:48
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