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2019 AMC 10A Problem 22

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2019 AMC 10A Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
Conditional Probability & States · difficulty 4 of 5 · about 6 min · position P21-25

Real numbers between 0 and 1, inclusive, are chosen in the following manner. A fair coin is flipped. If it lands heads, then it is flipped again and the chosen number is 0 if the second flip is heads and 1 if the second flip is tails. On the other hand, if the first coin flip is tails, then the number is chosen uniformly at random from the closed interval [0,1][0,1] . Two random numbers xx and yy are chosen independently in this manner. What is the probability that ∣x−y∣>12|x-y| > \tfrac{1}{2} ?

  1. A)

    13\frac{1}{3}

  2. B)

    716\frac{7}{16}

  3. C)

    12\frac{1}{2}

  4. D)

    916\frac{9}{16}

  5. E)

    23\frac{2}{3}

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