How do you find the blood type of a child whose parents are both type B blood.

If both parents of the child have type B blood, then the only two possible blood types that this child could have are either type B or type O.
One must consider the genotype (genetic makeup) of each parent when solving this question. The genotype for a person with type B blood is either homozygous B, where both of the parents contributed a gene for B to the offspring. This can be written as BB. Another possible genotype for a person with type B blood is heterozygous B, with one B and one O gene inherited from his or her parents. This can be written as BO. Since the genes for B are dominant to O, a person with a BO gene pair combination will exhibit type B blood in their phenotype.
If we do a genetics cross using a Punnett square, consider that, if each parent were heterozygous BO, their offspring would have the following probabilities for genotype: 25% will be homozygous BB, which is a person with type B blood, 50% will be heterozygous BO, which is a person with type B blood, and 25% will be homozygous OO, which is a person with the recessive type O blood.
Just to be clear, the ABO blood type in humans has three possible genes. A and B are co-dominant; however, each is dominant to O. That is why blood type AB exists: a person would need to inherit a gene for A and a gene for B from each parent to have type AB blood. I have attached a chart showing possible gene combinations and the blood types that they produce in people. A second link has the actual Punnett square that I have described worked out for you to see. It is the fourth problem on the image, bottom right hand side.
http://www.biology.arizona.edu/mendelian_genetics/problem_sets/monohybrid_cross/11t.html

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