Is this the same question as : what is the probablity that the test gives correct results ? We can also ask 3 other questions :
Another interesting question to ask is what is the single probablity of the tongue depressor to give accurate results ?
If we know that the tongue depressor has a 5% error on all students, sicks and non sicks, we can predict that the probability of being sick is (another rule here ? or another fashion of using the rule if applicable)
It would be nice to show how to go from 99.8% to the 500:1 ratio.