A hint to get started
Sum the chances of winning on successive rounds
Three people A,B,C roll a fair die for a prize. The first person to roll 6 wins. Each round proceeds A, B, C and repeats until someone wins. Find the probability that (i) A wins on the first throw, (ii) C wins on the first attempt, (iii) no one wins in a round, (iv) A wins.
CJC · Lecture · Example 11
Name the events, identify the sample space, and state which outcomes or conditions are being counted.