Probability Practice Test 1

Probability getting 6 white throwing a pair of dice $=\frac{5}{36}$
Probability of getting 7 white throwing a pair of dice $=\frac{6}{36}$
∴ Probability of winning A $=\frac{5}{36}+\frac{31}{36}\times \frac{30}{36}\times \frac{5}{36}$ $+\frac{31}{36}\times \frac{30}{36}\times \frac{31}{36}\times \frac{30}{36}$ $+\frac{5}{36}+...$
$=\frac{5}{36}\left[\frac{1}{1-\frac{31}{30}\times \frac{30}{36}}\right]$
$=\frac{5}{36}\times \frac{1296}{366}=\frac{30}{61}$
Probability of winning B = 1 - Probability of winning A $=1-\frac{30}{61}=\frac{31}{61}$