Final answer:
Joe has a 2/3 chance of being a carrier for cystic fibrosis since his brother is affected and both parents must be carriers of the recessive gene.
Step-by-step explanation:
Cystic fibrosis is an autosomal recessive condition, meaning that the disease manifests when an individual carries two recessive alleles (ff). If Joe's brother has cystic fibrosis, both their parents are carriers (Ff), as neither parent is affected by the disease. According to a Mendelian Punnett square, for two carrier parents, the possibilities for their children are as follows: 25% chance of being affected (ff), 50% chance of being a carrier (Ff), and 25% chance of being unaffected and not a carrier (FF).
Since Joe's brother is affected, Joe cannot be FF (which would mean he has no chance of being a carrier). Thus, we are focusing on the remaining 75%. As mentioned, out of this percentage, two-thirds would be carriers. Therefore, Joe has a 2/3 chance of being a carrier of the cystic fibrosis allele.