$A$ and $B$ throw a die alternately ($A$ throwing first) until one of them gets a six and wins the game. The probability that $A$ wins is:
Step-by-Step Solution
Key Concept: Write $P(A \text{ wins})$ as an infinite geometric series — $A$ can win on his $1^{\text{st}}$ throw, or his $2^{\text{nd}}$ (after both fail once), or his $3^{\text{rd}}$, and so on — then sum the series.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)