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2005 AMC 10A Problem 18

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2005 AMC 10A Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Conditional Probability & States · difficulty 4 of 5 · about 6 min · position P16-20

Team AA and team BB play a series. The first team to win three games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the individual games are independent. If team BB wins the second game and team AA wins the series, what is the probability that team BB wins the first game?

  1. A)

    15\frac{1}{5}

  2. B)

    14\frac{1}{4}

  3. C)

    13\frac{1}{3}

  4. D)

    12\frac{1}{2}

  5. E)

    23\frac{2}{3}

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