1.) Suppose there is an application which generates some banking related reports weekly, monthly, quarterly & yearly by doing some calculations. In this application, there is a fault while calculating yearly report. This is a high severity fault but low priority because this fault can be fixed in the next release as a change request.
2.) If we enter 100 characters of a letter to search in Search Engine. Suppose It does not support 100 characters and this engine starts crashing. One thing we have to notice that very less people will do like this type of activities. So this is a Low Priority and the defect is very high, So this is a High Severity. So this type of BUG is HIGH severity and LOW Priority