Assumptions:
(1) The obligate carrier parent for the woman has only 1 copy of the defective X-linked gene.
(2) The risk of inheritance is 0.5.
The prior risk if there are no affected grandsons is 0.5 for being a carrier and for being a non-carrier, based on the inheritance. If one or more grandsons are affected, then she is more likely a carrier, although the disorder could also be acquired as a new mutation.
conditional probability for being a carrier with normal grandsons =
= ((2^(number of normal grandsons))+1) / (2^((number of normal grandsons) + 1))
conditional probability for not being a carrier with normal grandsons =
= 1
posterior probability of being a carrier =
= (0.5 * ((2^(number of normal grandsons))+1) / (2^((number of normal grandsons) + 1))) / ((0.5 * ((2^(number of normal grandsons))+1) / (2^((number of normal grandsons) + 1)))+ 0.5)
posterior probability of being a noncarrier =
= (0.5 * 1) / ((0.5 * ((2^(number of normal grandsons))+1) / (2^((number of normal grandsons) + 1)))+ 0.5) =
= 1 - (posterior risk of being a carrier)
