Lements of rules affecting transferability of Negotiable Instruments

Now suppose that you go to your bank and write a check on your account payable to cash for $500. The teller gives you the cash without asking you to indorse the check. After you leave, the teller slips the check into his pocket. Later, the teller delivers it (without an endorsement) to his friend Carol in payment for a gambling debt. Carol takes your check to her bank, indorses it, and deposits the money.
Discuss whether Carol is a holder in due course.