If a mother is O positive, the father is B positive, and the baby is O negative, is that man the father of the baby?

If a baby's mother has an O positive blood type and a man has B positive blood type, it is possible for that man to be the baby's father if the child has O type blood or B type blood (either positive or negative). So, in short, yes, it is possible for him to be the father. However, it is not a guarantee—that blood type could be born to a mother with O negative blood type and a man with A, B, or O type blood. 

Blood typing can appear complicated, but it can be quite simply broken down by realizing what is possible and what is impossible based on genes provided by parents. The different types of blood are determined by either the presence or absence of certain antigens (an antigen is a substance in the blood that can activate an immune response if something foreign enters the blood). Certain blood types will or will not produce certain antigens, and that's how blood types can be relatively easy to determine.

For example, a person with type A blood has A antigens. A person with type B blood has B antigens. A person with type AB blood has both antigens, and a person with type O blood does not have any antigens.

If you have two parents with A blood, their child cannot have any other blood type besides A or O, because there's no way for B antigens to be produced; they can only come from an existing parent. 

If you have a parent with AB blood and a parent with A blood, the child can have A, B, or AB. 

It's possible for a child to have any of the four blood types (A, B, AB, or O) if one parent has A type and the other has B type.

The "positive" or "negative" delineation does not affect genetic typing of blood. A positive or negative indicates the presence or absence of another type of antigen called the Rh factor, which can be either present (positive) or absent (negative).

For example, someone with A+ blood has the A antigens and also carries the Rh factor antigen. Someone with A- blood has the A antigens but lacks the Rh factor.

Overall, looking at blood type is a good place to start in determining what the blood type of a child is likely to be based on the blood types of his/her parents. In the majority of cases, however, at least two blood types are possible, so it cannot be said for sure that an A parent and a B parent will create an AB child. The only time that a single blood type is possible as a result of two parents is an O type baby resulting from two O type parents.