 ### Description

If a woman is the daughter of an obligate carrier for an X-linked recessive disorder, and if she has only daughters as offspring, then the more unaffected grandsons she has, the lower the probability that she is a carrier for the condition.

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)