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2019 AMC 10B Problem 17

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2019 AMC 10B Problem 17AMC 10 Step by Step
Name:                             Date: September 13, 2026
Basic Probability · difficulty 3 of 5 · about 4 min · position P16-20

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 kk is 2−k2^{-k} for k=1,2,3,….k=1,2,3,\ldots. What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?

  1. A)

    14\frac{1}{4}

  2. B)

    27\frac{2}{7}

  3. C)

    13\frac{1}{3}

  4. D)

    38\frac{3}{8}

  5. E)

    37\frac{3}{7}

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