A research journal states: "Rejection rate for submitted manuscripts: 86%." A prospective author believes that the editor's statement reflects the probability of acceptance of any author's first submission to the journal. The author further believes that for any subsequent submission, an author's acceptance probability is 10% lower than the probability he or she had for acceptance of the preceding submission.
Thus, the author believes that the probability of acceptance of a first submission to the journal is 1 - 0.86 = 0.14, the probability of acceptance of the second submission is 10% lower, that is, (0.14)(0.90) - 0.126, and so on for the third submission, fourth submission, etc.
Suppose the author plans to continue submitting papers to the journal indefinitely until one is accepted. What is the probability that at least one paper will eventually be accepted by the journal?