Learn English – Should I use singular or plural after “there are many cases where”

grammatical-numberthird-person

Should I use singular or plural after "there are many cases where"?

Example:

There are many cases where patient/patients lack/lacks the required
knowledge yet they/she work/works it out.

As we are speaking generally in this kind of sentences, singular sounds more natural. But then is it OK as "cases" is plural?

Either form works, provided the singular form includes "a" in front of "patient":

There are many cases where a patient lacks the required knowledge yet s/he works it out.

Otherwise, the plural form would be preferable:

There are many cases where patients lack the required knowledge yet they work it out.