This has Base Rate Fallacy written all over it.

If you had a drunk-driver-detection machine that output "positive" 95% of the time when the driver is drunk and output "negative" 100% of the time when the driver is not drunk, and started administering the test to all drivers on a road, the probability that a positive detection is accurate is only 1.96%. That sounds exactly like what was happening: dragnet testing of bird droppings and little old ladies.

https://en.wikipedia.org/wiki/Base_rate_fallacy#Example_2:_D...

If simple statistics are difficult for people to understand, the Base Rate Fallacy is right out.