What is a problem
A problem is a cause of one or more incidents
Problems however are not incidents. An incident can raise a problem, specially if there is a high possibility that the incident might happen again. In the case of a server crash after office hours, the crash is a problem. This is a high priority problem because if this problem is not resolved, this will become an incident.
An incident does not become a problem. A problem may be raised because of an incident and as we've seen in the previous example, a problem may cause an incident.
You may raise a problem ticket and refer it to an incident.
The root cause of the problem may be known or not known. In any case, the following actions may be taken for problems:
Do nothing - if the problem does not affect the business, or if the cost of fixing the problem exceeds its benefits
Deploy work around if the determination of root cause exceeds the benefits.
Determine root cause and fix the problem if the benefit is worth it.