In The Tragical History of the Life and Death of Doctor Faustus, the main character makes a deal with the devil for power and knowledge. The play was written by Christopher Marlowe, a contemporary of Shakespeare, and premiered sometime in the late sixteenth century. In regards to the question, I'd respond with a question: Inherited from whom? We know very little of Faustus's background, except that he was "base of stock," and nothing about his family, so there is nothing to suggest the his sin is congenital. A second question is, what is meant by sin? Are we talking about the general sin that Christians believe all people are guilty of? Or are we talking about the specific sins of Faustus?
In answer to the first, Marlowe was accused of atheism, and while we can't be sure of his religious views, it seems unlikely that he would share the orthodox views of mainstream society. And despite how much the play is about good and evil, angels and devils, heaven and hell, it is by no means a "Christian" play. Marlowe is following the blueprint of tragedy by creating a character who incurs tragic consequences because of his pride. His specific sin, of course, is trading his soul for supernatural powers and more knowledge than his fellow students. And, while he is given chances to repent, he never does until it is too late. So I would say that Faustus's sin is wholly his own.