The first question is a little tricky, as it is tempting to think of it being equally likely that Susan is Brown-Blue than that she is Brown-Brown. But Blue-Brown is also a possibility that must be counted separately.

The second question is much more difficult, and I think there are a number of ways you could go wrong. On the surface, as Kimi points out, it seems that Jason’s brown eyes give us no new information. But while it is true that Ian’s eyes are not dependent on Jason’s, Jason’s brown eyes give us a bit more information about Susan. With each brown-eyed child she has without a blue-eyed one, it becomes slightly more likely that she is Brown-Brown.

David, for example, is one of five children, all of whom have brown eyes. So there is a 32/33 chance that his mother was Brown-Brown… assuming that a brown-eyed person in the general population is equally likely to be homozygous as heterozygous. If it’s actually 2/3, as above, then the chances of her being Brown-Brown would be 32/34, or 16/17.

As you might suspect by now, this story is entirely true, and I am Bill. According to Susan, Jason’s eyes are actually hazel-green and Ian’s eyes are brown.

And finally… Welcome, Little Fish! I know this sort of thing isn’t everyone’s cup of tea, but I’m sure you can appreciate the avuncular affection in trying to guess my nephews’ eye color before they were born.

Answers

Question 1: 1/6

Question 2: 3/20

i thought the 2nd question was a trick question, though, cuz i thought that the eyes of the 2nd kid weren’t dependent on the 1st kid’s eyes. although now that i think about it, i can see that if jason’s eyes were blue, that would change the odds of the 2nd kid’s eyes… that’s a good answer you got there =)

David carries the blue-eyed gene (he got it from his mom). Susan’s parents both carry the blue-eyed gene (they both gave it to her brother). This means that Susan has a 2/3 chance of carrying the gene, given that she has brown eyes.

So:
A) There’s a 1/3 chance that Susan doesn’t carry the blue-eyed gene.
B) There’s a 2/3 chance that she does.

If Susan carries the blue-eyed gene, the children have a 1/4 chance of being blue-eyed. So we can expand the above to:
A) 1/3 chance that Susan doesn’t carry the gene, so all her children are definitely brown-eyed.
B1) 1/2 (=2/3*3/4) chance that Susan carries the gene, but Jason has brown eyes anyway.
B2) 1/6 chance that Jason has blue eyes.

If Jason is brown-eyed, we’re in either situation A or B1, so there’s a 2/5 (=1/3 divided by 5/6) chance that Susan doesn’t carry the gene, and a 3/5 chance she does. So the odds that Ian has blue eyes are 3/5*1/4=3/20.