Those who have Medicare Advantage need to keep paying their Part A (if applicable) and Part B premiums because they still have a form of Medicare. When they pay their Medicare premiums, Medicare passes some of those funds to the insurance company that the senior chooses for their Medicare Advantage coverage. The only time that a senior with Medicare Advantage will not need to pay their Original Medicare premiums is if they qualify for and apply for the Medicare Savings Program and get some or all of their premiums covered by that program.