What are the chances that I will need a blood transfusion after delivery?

Fortunately it is . Not common. There can be severe uterine bleeding after delivery. Unlikely that you would lose enough blood from a "tear" to need a transfusion. As long as the bleeding is quickly controlled the team would try to avoid transfusion in an otherwise healthy mom.
2-10 % Postpartum hemorrhage may necessitate a blood transfusion. Postpartum hemorrhage is more common with c-sections than vaginal deliveries.