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AMC 10B 2019 #17 — Ball Toss into Bins Probability

1900SpecialistCombinatoricsProbability

AMC 10B · 2019 · Problem 17

A red ball and a green ball are randomly and independently tossed into bins numbered with positive integers so that for each ball, the probability that it is tossed into bin $k$ is $2^{-k}$ for $k=1,2,3,\ldots.$ What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?

Answer choices

A
\frac{1}{4}
B
\frac{2}{7}
C
\frac{1}{3}
D
\frac{3}{8}
E
\frac{3}{7}
0 students attempted0% solvedRating 1900

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