Assigning priority in testing play vital role in testing because it gives the idea to the developer which i have to be fixed first in this module or what are the critical errors to be fixed now Assigning priority Priority 1 - Critical/Fatal -- It should be fixed immediately Priority 2 - Major - It should be fixed before delivering to the customer priority 3 - Minor -- It should be fixed in the next module or omitted
Prioritising the tasks is the duty of Team lead if at all team lead assigns you to tasks at the same time and given some time in that case prioritise the tasks is team members duty.
For ex: If a team member having 2 tasks and need to start the testing at the same time first task for complete testing and 2nd one is just retesting only one issue in this case i can choose retesting as first task and go for 2nd task
So finally i can say one thing prioritising the tasks is completely depends on experience and date of delivery.