Answer:
1/4
Explanation:
The man is brown eyed so it can have both BB and Bb genotype but his mother was blue eyed and blue eyes is a recessive trait so his mother must have been bb. He would have got one "b" allele from her so his genotype must be Bb. Woman is also brown eyed with a blue type parent so her genotype must be Bb.
Bb X Bb :
B b
B BB Bb
b Bb bb
As evident, only 1/4 progeny will have recessive bb genotype which will result into blue eyes. So the probability that this couple will have a blue-eyed child is 1/4.