Blue eye colour in human is recessive to brown eye colour. The expected children of a blue-eyed woman and a brown-eyed man who had a blue-eyed mother is likely to be in the ratio of:
One blue-eyed and one brown-eyed
The recessive character is expressed only in homozygous condition. Thus, blue-eyed woman will have 'bb' genotype, while brown-eyed man may have 'BB' or 'Bb' genotype. But the man had a blue-eyed mother, so, he will have 'Bb' genotype. It can be explained as follows: