If a child got a brown-eyed allele from dad (B) and a blue-eyed allele from mom (b), what color eyes will they have (Bb)?

Brown

Dominant means that if at least 1 of your two copies is brown (Bb), then you will have brown eyes. Geneticists represent the different versions of the eye colour gene as B for brown and b for blue (the capital letter is the dominant, the lowercase, recessive). So brown eyes are either Bb or BB and blue eyes are bb.