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Flora Frog Number Line Jump

1675AdeptCombinatoricsAlgebraProbability

AMC 12A · 2023 · Problem 17

Flora the frog starts at $0$ on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $m$ with probability $\frac{1}{2^m}$. What is the probability that Flora will eventually land at $10$?

Answer choices

A
\frac{5}{512}
B
\frac{45}{1024}
C
\frac{127}{1024}
D
\frac{511}{1024}
E
\frac{1}{2}
0 students attempted0% solvedRating 1675

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