avasalie

I am an instructor having a Problem trying to reconcile the sum rule with the answer to this Q: if a blue eyed (bb) woman marries a man with brown eyes (B?) where his genotype is unknown, what is the probability of having a blue-eyed child? I calculate it at 1/4 because he has 1/2 chance of being Bb and 1/2 chance of passing it on. But if you consider it as mutually exclusive he is either BB OR Bb, then if he is BB there is 0 chance of blue eyed child OR if he is Bb, there is 1/2 chance of blue eyed child, then 0 + 1/2 = 1/2. What is wrong here?