Enigmas & puzzles

June 18, 2005
Pigfungler's syndrome

"I'm becoming concerned about the incidence of Pigfungler's syndrome," said the Acrimonian health minister. "What are the latest figures, Bertram?"

"Out of a total population of 200 million, it is estimated that half a million Acrimonian citizens suffer from PS, minister. The figure is based on random testing of a representative sample, but it's probably quite accurate."

The minister stared at him. "But that doesn't tell us which people have the disease, Bertram! We must initiate a program of testing for all citizens!"

"The most accurate test available was devised by Professor Gnutter's team," his secretary said. "It detects 90 per cent of cases among those individuals who do have PS, and gives false positives for only 1 per cent of those individuals who do not."

"That's good, isn't it?" said the minister brightly. "We must go ahead immediately with a crash programme to test everybody!"

Bertram tugged at his ear, as if deep in thought. "I'm not sure that's wise, minister."

"Why ever not, man?"

"Well… you promised in your radio broadcast last week that you wouldn't alarm people with wrong diagnoses. You said that you would only institute a full-scale testing programme if the rate of false positives—the proportion of people wrongly tested positive for PS out of the total number that test positive—was less than 20 per cent."

"So? Professor Gnutter's test clearly performs a lot better than that!"

Bertram grimaced. "Er—I'm not sure that it does, actually, minister."

Who is right: Bertram or the minister?

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The answer

Bertram is right.

Out of 500,000 people with PS, 450,000 will test positive. Out of 199,500,000 people not suffering from PS, 1,995,000 will test positive. The test will give a false positive in 1.995 million cases out of a total of 2.445 million, a failure rate slightly more than 81 per cent.

The winner is Giles Cattermole, Cardiff