First of all, the probability of getting 6 every time you roll the dice is 1/6.
Then look at A, the first time 1/6, the third time (5/6) 2 * 1/6 and the fifth time (5/6) 4 * 1/6.
We can find that it is a geometric series with infinite terms, a 1= 1/6 and q=25/36.
Total sa = a1(1-q) = 6/11.
B The probability of victory is obviously 1-Sa=5/ 1 1.
If you want to calculate, it is b 1=5/6* 1/6, q=25/36, and sb = 5/1.