Final answer:
The probability that June and Sheldon's daughter will have Becker muscular dystrophy is near 0, as she cannot inherit the affected X chromosome from her father due to the mechanics of X-linked recessive inheritance.
Step-by-step explanation:
The subject of this question concerns the probability that June and Sheldon's daughter would have Becker muscular dystrophy (BMD), an X-linked recessive condition. Since June's two brothers are affected and her parents are phenotypically normal, June is most likely a carrier of the BMD gene. Seeing as Sheldon is affected with BMD, he has one X chromosome with the BMD gene. Their daughter would have BMD only if she inherits the X chromosome with the BMD gene from both parents.
However, since the daughter receives one Y chromosome from Sheldon, making her female, she does not inherit Sheldon's X chromosome with the BMD gene. Instead, she receives his Y chromosome. Thus, for the daughter to be affected, she would need to inherit the BMD gene from June if June indeed is a carrier. The chance that the daughter is a carrier of the disease (inherits the BMD gene from June) is 1/2, whereas the chance that she is affected (inherits the BMD gene from both June and Sheldon) is near 0 because she can't inherit an affected X chromosome from Sheldon.
The correct answer to the question 'What is the probability that this daughter will have BMD?' is a. Near 0, given the circumstances of X-linked recessive inheritance and the fact that the father (Sheldon) cannot pass on his affected X chromosome to a daughter.