Mathematics - Probability Question with Solution | TestHub

A's chance of winning in a throw $=\frac{5}{36},$ B's chance of winning in a throw $=\frac{1}{6}$

A's chance of losing in a throw $=\frac{31}{36},$ B's chance of losing in a throw $=\frac{5}{6}$

A can winning the game $=\frac{5}{36}+\frac{31}{36}\times \frac{5}{6}\times \frac{5}{36}+\frac{31}{36}\times \frac{5}{6}\times \frac{31}{36}\times \frac{5}{6}\times \frac{5}{36}+----$ $=\frac{5}{36}\left[1+\frac{155}{216}+{\left(\frac{155}{216}\right)}^2+----\right]=\frac{30}{61}$