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Wed 25 Mar, 2015 07:22 pm
Problem trying to reconcile sum rule with 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 iif 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?
@avasalie,
avasalie wrote:What is wrong here?
What's wrong is that you're only considering half of the equation.
He's Bx.
If he's BB there's four combinations that would result in brown eyes:
Bb, Bb, Bb and Bb.
If he's Bb there's two combinations that would result brown eyes and two combinations that would result in blue eyes:
Bb, Bb, bb and bb.
That's two out of eight total chances, or 2/8. And 2/8=1/4.
@InfraBlue,
THANKS for the confirmation! that was what i calculated, but my students were very confused as to why the sum rule didn't work here. It doesn't apply in this case as stated above because you have to consider ALL possible genotypes when one parent is unknown.
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