It's possible. It is an inherited disease and prevalent in some populations. You probably would have benefited from genetic counseling before getting pregnant. See the quote that follows, (it is only about beta thalassemia and there are several other kinds):
"When two members of a couple carry the beta thalassemia trait, there is a 25% chance that each of their children will inherit beta thalassemia disease by inheriting two beta thalassemia mutations, one from each parent. The clinical severity of the beta thalassemia disease—whether an individual has beta thalassemia intermedia or beta thalassemia major—will depend largely on whether the mutations inherited are beta0 thalassemia or beta + thalassemia mutations. Two beta0 mutations generally lead to beta thalassemia major, and two beta+ thalassemia mutations generally lead to beta thalassemia intermedia. Inheritance of one beta0 and one beta + thalassemia mutation tends to be less predictable."
I think I have also seen references to alpha thalassemia, delta thalassemia, and maybe others. Please check with your doctor, this is not something that can be answered accurately online.
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