This is based on a true situation.
A guy I know was about to get engaged when they submitted their numbers to Dor Yeshorim and were told that they are probably not compatible.
The test that Dor Yeshorim performed had a 4% rate of false positives for the genetic disorder that they both tested positive for (in other words there was a 4% chance that he was not a carrier and a 4% chance that she was not a carrier). The rov that called them informed them that there is a much more expensive test that is 100% accurate.
Before spending over $1,000 on the test, he wanted to know the probability that they would be compatible.
What are the chances that they are compatible?