smc

The probability that Carol wins during the first cycle through is $\frac{5}{6}\ast \frac{5}{6}\ast \frac{1}{6}$, and the probability that Carol wins on the second cycle through is $\frac{5}{6}\ast \frac{5}{6}\ast \frac{5}{6}\ast \frac{5}{6}\ast \frac{5}{6}\ast \frac{1}{6}$. It is clear that this is an infinite geometric sequence, and we must find the sum of it in order to find the answer to this question. Thus we set up the equation: $\frac{\frac{25}{216}}{1-\frac{125}{216}}$, or $\frac{\frac{25}{216}}{\frac{91}{216}}$, which simplifies into $\boxed{\frac{25}{91}}$