Final answer:
Bill's filing status would most likely be 'Head of Household' since he is unmarried, supports his mother who has no income, and meets the requirements to file as Head of Household.
Step-by-step explanation:
Bill's filing status would most likely be 'Head of Household.' According to the Internal Revenue Service (IRS), to be considered as Head of Household, you need to be unmarried or legally separated from your spouse, and you must have paid more than half the cost of keeping up a home for yourself and your qualifying dependent. In this case, Bill can claim his mother as a dependent since he fully supports her and she has no income. Therefore, he meets the requirements to file as Head of Household.