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First-Roll Wins Probability

MediumStatistics & Probability00:00
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Your question is First-Roll Wins Probability. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

Two players take turns rolling a fair six-sided die. The first player to roll a 6 wins. What is the probability that the first player wins?

Express the answer as an exact fraction and decimal. Show how you account for repeated rounds in which neither player rolls a 6, and state the assumptions about independence and indefinite play.