Polydactyly can be dominant or recessive. that is
- A single copy of the mutation/s involved result in the phenotype
- Both copies of the gene must be mutated to result in the phenotype
When two random people who don't have polydactyly nor a family history of polydactyly have a child, there is around 1/548 (0.18%) chance that child will be polydactyly because the parents were carriers without knowing it, and a 1/11.7 (8.54%) chance the child is a carrier of a single copy
If the aunt's polydactyly is Dominant, then your friend's father hasn't inherited it (he isnt polydactyly) and just has the normal population chance of being a carrier.
In the case of Dominant polydactyly, assuming your friend has a partner with no history of polydactyly, your friend and her partner have the same chance as average of a polydactyly child (1/548)
If the aunt's polydactyly is recessive, meaning she has two copies one from each parent (you friend's grandparents), there is a 1/130 (0.76%)chance your friend's child will have polydactyly (4.2 times more likely), and a 1/4.5 (21.4%) chance of being a carrier (2.6 times more likely)
I'll quickly go through the working/
if you're interested:
Given that the grandparents are both carriers (needed for the aunt to have two copies), then your friend's father has a 2/3 chance of being a carrier of a single copy (1/3 chance no copies, 0/3 chance having two copies because he isn't polydactyly).
Your friend's mother has the usual 1/11.7 chance of being a carrier.
The chance of your friend inheriting a single copy is (chance passes from father) + (chance passes from mother) - (chance of getting two copies)
=0.6600/2 + 0.0854/2 - (0.33*0.0427)
=0.3727 - 0.0140
35.9% chance your friend carries one copy
Your friend has 1/2.8 chance of carrying and 1/5.6 of passing it on
Friend's partner has the 1/11.7 chance of being a carrier and the 1/23.4 chance of passing it on
Therefore their child has
=0.1793*0.0427 (chance friend passes on * chance partner passes on)
=1/130 chance of having two copies, having polydactyly
=0.1793 + 0.0427 -(0.1793*0.0427) (chance any copies - chance two copies)
=1/4.7 chance of one copy a 2.5 times increase risk