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A man with a blood type AB mates with a women with a blood type A and produced a kid with a blood type B

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That happens because he has AB blood and she has A so when they mate the kid will have Type B blood basically she took away the A from him
Sorry if I'm wrong next time give a little more info

The wife is heterozygous for Type A (writen as AO or Ai when completing Punnett squares), meaning she carries one allele for A and one allele for O.  During fertilization, the offspring received a dominant allele for Type B blood from the father and a recessive allele for Type O blood from the mother.