Can a father with AB- blood type and a mother with an O- blood type have a child with O- type?

The answer is NO .
Person with AB blood group is genetically having two dominant alleles for determination of AB blood type. Person with O blood group on the other hand is double recessive.
Thus each of their progeny will receive one dominant allele and one recessive allele. Each child may show either A blood type or B blood type: probability will be 50/50.

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