**Answer is (4) **\(\frac{31}{61}\)

P(A) = \(\frac{5}{36}\), P(B) = \(\frac{1}{6}\)

P(A wins) = W + FFW + FFFFW + .........

**= \(\frac{5}{36} + \frac{31}{36} \times \frac{5}{6} \times \frac{5}{36}\)+ \(\frac{31}{36} \times \frac{5}{6} \times \frac{31}{36} \times \frac{5}{6} \times \frac{5}{36} + ........\)**

**= \(\frac{\frac{5}{36}}{1-\frac{31}{36} \times \frac{5}{6}}\)**

**= \(\frac{\frac{5}{36}}{\frac{36 \times 6 - 31 \times 5}{36 \times 6}}\)**

= \(\frac{30}{216-155}\)

= \(\frac{31}{61}\)