Thalassaemia is due to the defect in the production of globin chains in haemoglobin. If the defect is in the alpha globin chain, it is said to be the alpha thalassaemia, otherwise, it is the beta thalassaemia.
The defected gene is recessive. Normal person would have all these genes normal. The person having two defected genes for the same globin chain will have seere anaemia and need to have blood transfusion for the whole life. It is said to be the major thalassaemia. If only one gene is defected, then, it is the minor thalassaemia. The patient of minor thalassaemia would have no symptom or mild anaemia.
Reference :
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(book)
Advanced level Biology for Hong Kong, Bk 2, by Y.K. Ho, Manhattan Press, pp. 216