A field test for a crop disease correctly identifies the disease in 95 of every 100 infected plants and wrongly reports the disease in 5 of every 100 healthy plants. In one grower's field only about one plant in every thousand is infected. The grower argues that a plant his test reports as infected is almost certainly infected. Which of the following best explains why the grower is mistaken?

Take 100,000 plants: about 100 are infected, of which the test flags 95; the other 99,900 are healthy, of which 5 per cent - nearly 5,000 - are flagged wrongly. So barely 2 in every 100 flagged plants are actually infected. When the condition is rare, a small error rate applied to a very large healthy group swamps the true detections. The other options question the tester or the test in general instead of explaining the arithmetic.