Management Aptitude Test Dec 2012 Paper

(b) Probability of getting 6 while throwing a pair of dice = $\frac{5}{36}$
Probability of getting 7 while throwing a pair of dice = $\frac{6}{36}$
Therefore, probability of winning A = $\frac{5}{36}+\frac{31}{36}\times \frac{30}{36}\times \frac{5}{36}$+$\frac{31}{36}\times \frac{30}{36}\times \frac{31}{36}\times \frac{30}{36}\times \frac{5}{36}$+.........
= $\frac{5}{36}\left[\frac{1}{1-\frac{31}{36}\cdot \frac{30}{36}}\right]$ = $\frac{5}{36}\left[\frac{1296}{1296-930}\right]$
= $\frac{5}{36}\times \frac{1296}{366}$ = $\frac{5\times 36}{366}$ = $\frac{5\times 6}{61}=\frac{30}{61}$
and probability of winning B= 1 - Probability of winning A
= 1 - $\frac{30}{61}=\frac{31}{61}$