Die Roll Until Odd Expected

1425ApprenticeCombinatoricsProbability

AMC 10B · 2021 · Problem 18

A fair $6$-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?

Answer choices

~\frac{1}{120}

~\frac{1}{32}

~\frac{1}{20}

~\frac{3}{20}

~\frac{1}{6}

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