No. The child would receive type a antigens from both of their parents and no type b antigens.
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the answer to this is purely psychological. For example, by implying that the person supposed to answer this will not in fact answer it makes this a negative question. However, by adding the question...
It could be A (25%) or B (25%) or AB (25%) or O (25%) blood group
The father must have a blood type of B or AB.