Tilly could have blood type A, B, or AB.
Tilly's mother has blood type A, which means she must have the genotype AA or AO. Tilly's father has blood type B, which means he must have the genotype BB or BO.
When Tilly's parents' genes combine, there are three possible outcomes:
One possible outcome is IA from the mother and I^B from the father, resulting in the genotype I^IB, which is blood type AB. Another possible outcome is IA from the mother and I from the father, resulting in the genotype I^I, which is blood type A.
The last possible outcome is I from the mother and I^B from the father, resulting in the genotype AO, which is also blood type A.
In conclusion, Tilly can have blood type A, B, or AB.